SB    ShH    It  3 


UNIVERSITY  OF  CALIFORNIA. 


GIFT  OF 


« 


Class 


THE  INTERNATIONAL  SCIENTIFIC  SERIES. 
VOLUME  XVIII. 


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TABLE  OF  SPECTRUM  ANALYSIS. 

1  SOI.AI:  SPECTRUM,  'i.  -  It  SPECTRA  of  VARIOUS  METALS.   12  HYDROGEN.    13  NITKOGKN. 

10  20  30  *>  30  60  70  80  80          100          111)         120         130          140          liO         1BO          170 


THE    INTERNATIONAL   SCIENTIFIC   SERIES. 


THE  NATURE  OE  LIGHT, 


WITH  A  GENERAL  ACCOUNT  OP 


PHYSICAL    OPTICS. 


BY 

DR.   EUGENE   LOMMEL, 

PROFESSOR  OF  PHYSICS  IN  THE  UNIVERSITY  OF  ERLANGEN. 


WITH  ONE  HUNDRED  AND  EIGHTY-EIGHT  ILLUSTRATIONS  AND  A  PLATE  OF  SPECTRA 
IN  CHROMOLITHOGRAPHY. 


J 


NEW  YOKE: 
D.    APPLETON    AND    COMPANY, 

72    FIFTH    AVENUE. 
1898 


PREFACE. 


THE  OBJECT  of  this  little  work  is  to  give  to  a  large 
circle  of  readers  an  answer,  based  on  the  present  state 
of  science,  to  the  question,  What  is  the  Nature  of 
Light? 

In  the  first  fourteen  Chapters  the  laws  of  reflexion, 
refraction,  dispersion,  and  absorption  of  light  are  demon- 
strated by  experiment  without  reference  to  any  theory 
of  the  nature  of  light.  This  comes  forward  prominently 
for  the  first  time  in  the  fifteenth  Chapter,  in  discussing 
Fresnel's  mirror  experiment,  and  the  conclusion  arrived 
at  being  in  favour  of  the  undulatory  theory,  it  is  shown 
that  this  theory  is  not  only  in  accordance  with  all  the 
facts  hitherto  known,  but  also  affords  the  most  satis- 
factory explanation  of  the  phenomena  of  double  "Re- 
fraction and  polarisation,  both  of  which  receive  subse- 
quent consideration. 

Mathematical  reasonings  are  wholly  omitted  in 
the  text ;  where  these  are  required  or  appear  to  be 
desirable  for  the  more  thorough  and  complete  knowledge 
of  the  phenomena  described,  they  are  given  in  the  most 

L32586 


vi  PJIKFACE. 

elementary  form,  and  are  added  as  an  appendix  to  the 
Chapters.* 

Numerous  wood-cuts  are  introduced,  many  of  which 
are  taken  from  the  Atlas  of  Physics  of  Johann  Muller ; 
the  majority,  however,  are  new,  as  is  also  a  chromo- 
lithographic  plate  of  spectra. 

I  trust  that  tkte  attempt  to  render  a  branch  of 
Physics,  which  at  first  sight  seems  from  its  delicate 
nature  to  lie  somewhat  beyond  the  grasp  of  the  general 
public,  intelligible,  will  meet  with  a  kindly  reception 
and  consideration  at  their  hands. 

ERLANGEN,  July  1874. 


*  The  theory  of  spherical  mirrors  find  lenses,  for  example,  and  the 
elementary  theory  of  the  rainbow,  are  added  as  Appendices  to  the  Chapters 
f.n  which  these  subjects  are  discussed. 


CONTENTS. 


CHAPTEP  PAOH 

PREFACE     .                  v 

I.     SOURCES  OF  LIGHT 1 

II.     RECTILINEAR  PROPAGATION  OF  LIOHT         .         .        .         .14 

III.  REFLEXION  OF  LIGHT 26 

IV.  SPHERICAL  MIRRORS 40 

APPENDIX  TO  THE  FOURTH  CHAPTBR 5C 

V.     REFRACTION 56 

APPENDIX  TO  THE  FIFTH  CHAPTER 73 

VI.     LENSES 78 

APPENDIX  TO  THE  SIXTH  CHAPTE.K        .         .         ...  90 

VII.     OPTICAL  INSTRUMENTS 95 

VIII.     DISPERSION  OF  COLOUR 112 

APPENDIX    TO   THE    EIGHTH    CHAPTER:    THEORY    OF    THE 

RAINBOW 126 

IX.     ACHROMATISM         . 134 

APPENDIX  TO  THE  NINTH  CHAPTER.     ACHROMATIC  LENSES  146 


mi  CONTENTS. 

CHAFFER  PAGK 

X.  SPECTRUM  ANALYSIS 148 

XI.  SPECTBUM  ANALYSIS  OF  THE  SUN       .         .         .         .         .159 

XII.  ABSOBPTION ....  172 

XIII.  FLUORESCENCE.    PHOSPHORESCENCE.     CHEMICAL  ACTION     ,  183 

XIV.  ACTION  OF  HEAT ,        .        .197 

XV.  FRESNEL'S  MIRROB  EXPERIMENT  :  UNDULATORY  MOVEMENT  207 

XVI.  PRINCIPLE  OF  INTERFERENCE.     CONSEQUENCES  OF  FRESNEL'S 

EXPERIMENT 217 

XVII.  HUYGHENS'  PRINCIPLE         .         .         .         .         .         .         .  229 

XVIII.  DISPERSION  OF  LIGHT.  ABSORPTION  .  .  ...  242 

XIX.  DIFFRACTION  OF  LIGHT 258 

XX.  COLOURS  OF  THIN  PLATES 273 

XXI.  DOUBLE  DIFFRACTION  OF  LIGHT 282 

XXII.  POLARISATION 293 

XXIII.  POLARISING  APPARATUS 303 

XXIV.  INTERFERENCE  OWING  TO  DOUBLE  REFRACTION      .         .     .  316 
XXV.  CIRCULAR  POLARISATION 332 

INDEX           .                                                                           ,  853 


LIST   OF  ILLUSTRATIONS. 


wo.  PAOS 

1.  Bunsen's  burner 3 

2.  Oxygen  lamp 6 

3.  Drummond's  light  .         .         .                  .         .         .         .         .  6 

4.  Magnesium  light 8 

5.  Electric  light  between  carbon  points        .         .         .         .         .  8 

6.  Electric  lamp 11 

7.  Shadows 15 

8-9  Shadow  nucleus,  and  penumbra 16 

10.  Projection  of  an  image  through  a  small  aperture       ...  20 

1 1.  Diminution  of  illumination  in  the  ratio  of  the  square  of  the 

distance 22 

1 2.  Bunsen's  photometer        .         .         .         .         .         .         .         .23 

13.  Rumford's  photometer         .         .         .         .         .         ...  24 

14.  Reflexion  of  light .         .         .26 

15.  Model  to  demonstrate  the  law  of  reflexion  of  light        .         .     .  28 

1 6.  Production  of  image-point  in  a  plane  mirror    ....  29 

17.  Production  of  the  image  in  a  mirror             30 

18.  Mirror-image  in  a  transparent  plate  of  glass  .         .         .31 

19.  Heliostat             32 

20.  Reusch's  heliostat 33 

21.  Principle  of  reflecting  goniometer 34 

22.  Angular  mirror 36 

23.  Principle  of  the  mirror  sextant             37 

24.  Mirror  of  reflecting  sextant      .......  38 

25.  Concave  mirror            .........  40 

26.  Focus 41 

27.  Conjugate  foci              42 

28.  Conjugate  points               44 

29.  Conjugate  points  on  a  secondary  axis 45 

30.  Real  image 46 

31.  Mode  of  production  of  real  images 46 


C  LIST  OF  ILLUSTRATIONS. 

FIG.  PAGE 

32.  Mode  of  formation  of  virtual  image          .....  48 

33.  Virtual  principal  focus  of  a  convex  mirror 49 

34.  Production  of  a  virtual  image  behind  a  con  vex  mi  rror                .  50 

35.  Mode  of  expressing  the  size  of  any  angle 50 

36.  Determination  of  the  position  of  the  principal  focus          .         .  51 

37.  Determination  of  the  position  of  conjugate  points        .         .     .  52 

38.  Construction  showing  the  formation  of  the  image     ...  54 

39.  Eefractor 56 

40.  Angles  of  incidence  and  of  refraction 57 

41.  Apparatus  for  demonstrating  the  la AV  of  refraction       .  58 

42.  Law  of  refraction 60 

43.  Total  reflexion 61 

44.  Totally  reflecting  prism 64 

45.  Apparent  position  of  a  point  situated  beneath  the  surface  of 

the  water    ...» 65 

46.  Appearance  presented  by  a  rod  dipped  in  water        .         .         .65 
47-  Kefraction  through  a  transparent  plate  with  parallel  surfaces  65 

48.  Refraction  through  two  parallel  plates 67 

49.  Refraction  through  a  piece  of  glass  the  surfaces  of  which  are 

not  parallel 68 

50.  A  prism 68 

51.  Deflection  through  a  prism 69 

52.  Smallest  deflection  through  a  prism     .         .         .         .         .     .  70 

53.  Hollow  prism .         .71 

54.  Construction  of  the  refracted  ray         .         .         .         ,  73 
65.  Rf  fraction  through  two  parallel  plates      .         .         ...  74 

56.  Passage  of  a  ray  of  light  through  a  prism 76 

57.  Convex  lenses 78 

58.  Concave  lenses             .........  7?» 

59.  Axis  and  centres  of  curvatures          ......  79 

60.  Focal  point 80 

61.  Conjugate  foci          ...                  .....  81 

62.  Conjugate  foci 82 

63.  Virtual  image 82 

64.  Production  of  a  real  image .84 

65  Real  image  seen  through  a  convex  lens 86 

66  Virtual  image  with  a  convex  lens 87 

67.  Virtual  focus  of  a  concave  lens 88 

68.  Action  of  a  concave  lens  on  convergent  and  divergent  rn  ys        .  89 

69.  Virtual  image  formed  by  a  concave  lens 8S 

70.  Determination  of  the  focal  distance 90 

71.  Determination  of  conjugate  points    ......  93 

72.  Dubosq's  lamp 95 


LIST   OF  ILLUSTRATIONS.  xi 

pro.  PAGB 

73.  Magic  lantern 97 

74.  Solar  microscope 99 

75.  Camera  obscura       .         .         .         .         .         .         .         .         .101 

76.  Action  of  the  microscope 102 

77.  Microscope 103 

78.  Mode  of  showing  the  image  of  a  microscope  as  an  object       .     .     104 

r9.     Action  of  the  astronomical  telescope 105 

8C      Astronomical  telescope J  06 

B\  Instrument  for  measuring  the  prismatic  deflection    .         .         .     106 

82.     Terrestrial  telescope .         .         .     .     107 

S3.  Construction  of  Galileo's  telescope            .         .         .         .         .108 

84.     Galileo's  telescope 108 

35.  Action  of  Newton's  reflecting  telescope     .                  ...     109 

86.  Action  of  the  reflecting  telescope  with  front  opening     .         .     .     110 

87.  Gregory's  reflecting  telescope .110 

88.  Action  of  Gregory's  reflector Ill 

89.  Vaporisation  of  metal  in  the  arc  of  the  electric  flame        .         .112 

90.  Different  deflection  of  different  coloured  rays  of  light  .         .     .     115 

91.  Undecomposability  of  the  colours  of  the  spectrum    .         .         .118 

92.  Impure  spectrum  obtained  by  the  use  of  a  circular  opening       .     119 

93.  Combination  of  the  colours  of  a  spectrum  to  form  white  light  .     119 

94.  Complementary  colours 120 

95.  Combination  of  two  homogeneous  colours          .         .         .         .121 

96.  Refraction  and  internal  reflexion  in  a  rain-drop  .         .     .     123 

97.  Refraction  and  double  internal  reflexion  in  a  rain-drop     .         .     124 

98.  Mode  of  formation  of  the  rainbow        .         .         .         .  125 

99.  Refraction  and  internal  reflexion  in  a  drop  of  water          .         .     1-6 

100.  Theory  of  the  rainbow 129 

101.  Combination  of  two  similar  prisms  without  deflection  and  with- 

out dispersion.         ........     136 

102.  Combination  of  a  crown  and  flint-glass  prism  causing  disper- 

sion but  no  deflection 137 

103-4.  Combinations  of  prisms  which  cause  no  deflection  .         .     138 

105.  Combination  of  a  crown  and  flint-glass  prism,  with  deflection, 

but  without  dispersion  (an  achromatic  prism)       .         ..138 

106.  Spectrum  thrown  by  crown  glass  and  by  flint  glass  .         .139 

107.  Dispersion  of  colour  of  a  lens      .         .         .         .         .  140 

108.  Achromatic  lens .         .         .141 

109.  Measurement  of  refraction  as  practised  by  Fraunhofer          .     .     142 

110.  Spectrometer  .         .         . 144 

111.  Bunsen's  spectroscope 148 

112.  Induction  apparatus 154 

113.  Geissler's  gpectruin  tube  .  155 


Xli  LIST  OF  ILLUSTRATIONS. 

FIO.  PAGB 

114.  Action  of  the  comparison  prism       .          .         .         ,         ,         .159 

115.  Comparing  prism  at  the  slit  of  the  spectroscope   .         .         .     .  160 

116.  Bunsen's  apparatus  for  the  absorption  of  Sodium  light     .         .162 

117.  Absorption  of  the  Sodium  flame  .         .         .         .         .     .  163 

118.  Telescope  with  four  prisms 166 

119.  Absorption  spectra  of  nitrous  oxide  and  of  the  vapour  of  iodine  173 
120      Absorption  spectra 175 

121.  Absorption   of  the   colouring  matter   of  litmus  with  different 

thicknesses  of  the  layer 178 

122.  Fluorescence 183 

123.  Solar  spectrum  with  the  ultra-violet  portion     .         .         .         .185 

124.  Geissler's  fluorescence  tube 188 

125.  Geissler's  tube  with  Uranium  glass  spheres       ....  188 

126.  Absorption  and  fluorescing  spectrum  of  Naphthalin-red        .     .  190 

127.  Construction  of  the  thermopile         »,  .         .         .         .  199 

128.  Linear  thermopile       .         .         .         .         .         .         .         .     .  199 

129.  G-alvauometer          «... 200 

130.  Heat-curves  of  the  spectra  thrown  by  flint  glass  and  rock  salt .  201 

131.  Action  of  the  invisible  thermotic  rays 202 

132.  Light,  heat,  and  photographic  action  of  the  solar  spectrum       .  205 

133.  Fresnel's  mirror           .        T   ..•;.'.• 207 

134.  Fresnel's  mirror  experiment    .         .      .  .         .     :    .         .         .  208 

135.  Undulatory  ray .         .                  216 

136.  Interference  of  two  systems  of  waves 218 

137.  Huygheus'  principle 230 

138.  Explanation  of  reflexion  and  refraction    .         .         .         .         .  234 

139.  Impact  of  elastic  balls         .         .         .         .         .         ...  238. 

140.  Unusual  dispersion  power  of  Fuchsin 243 

141.  Tuning  fork •    .         .     .  251 

142.  Diffraction  or  inflection  image  of  a  narrow  slit          .         .         .  258 

143.  Di ffraction  apparatus .         »       „        •        ,         .         .         .     .  260 

1 44.  Phenomena  of  diffraction  with  a  circular  aperture   ....         .  260 

145.  Phenomena  of  diffraction  with  a  rhomboidal  aperture .         .     .  260 

146.  Explanation  of  diffraction  through  a  slit          ....  262 

147.  Diffraction  phenomena  through  a  grating 266 

148.  Explanation  of  diffraction  through  a  grating    ....  267 

149.  Comparison  of  the  prismatic  with  the  grating  spectrum        .     :  271 

150.  Newton's  colour  glass 273 

151.  Newton's  coloured  rings      .                  274 

152.  Explanation  of  the  colours  of  thin  laminae       ....  275 

153.  Interference  striae  in  the  spectrum 280 

154.  Double  refraction  in  Iceland  spar 283 

155.  Rhombohedron  ...  ,  284 


LIST   OF  ILLUSTRATIONS.  Xlii 

no.  PAOH 

156.  Crystalline  forms  of  Iceland  spur 2H5 

1 57.  Double  refraction.     First  case 286 

1 08.     Double  refraction.     Second  case 287 

159.  Double  refraction.     Third  case .  288 

160.  Wave-surface  of  a  negative  uniaxial  crystal  .  289 

161.  Huyghens'  construction  of  double  refraction        .         .         .     .  290 

162.  Two  rhombohedra  of  Iceland  spar 293 

163.  Polarised  ray  of  light          .         .         .         .         .         .         .     .  298 

164.  Nicol's  prism 304 

1  Go.     Polarisation  by  reflexion 306 

166.  Two  polarising  mirrors 307 

167.  Biot's  polarising  apparatus 307 

1 68.  Norremborg's  polarising  apparatus  .....  309 

169.  Norremberg's  polarising  apparatus,  with  glass  laminae          .     .  311 

170.  Tourmaline  tongs 314 

171.  Parallel  Tourmaline  plates 315 

172.  Crossed  Tourmaline  plates 315 

173.  Two  Nicol's  prisms  employed  as  a  polariser         .         .         .     .  316 

174.  Decomposition  of  vibrations    .         .         .         .         .         .         .3.7 

1 75.  Dubosq's  polarising  apparatus 325 

176.  E ings  of  colour  produced  by  uniaxial  crystals          .         .         .  328 

177.  Rings  of  co'our  produced  by  biaxial  crystals       .         .         .     .  328 

178.  Polarisation  image  of  suddenly  cooled  plate  of  glass         .         .  330 

179.  Two  Nicol's  prisms 332 

180.  Rotation  of  the  planes  of  vibration  in  Quart/ .          .         .         .  334 

181.  Circular  movement  of  pendulum 336 

182.  Decomposition  of  vibrations 338 

183.  Effect  of  two  opposite  circular  vibrations 342 

184.  Double  prism  of  Quartz 344 

185.  Tube  for  the  reception  of  circularly  polarising  fluids    .         .     .  347 

186.  Double  plate  of  right  and  left  rotating  Quartz          .         .         .  348 
187  Soleil's  Saccharimeter .         .         .         .         .         .         ,         .     .  349 

186      Compensator 350 


OPTICS. 


CHAPTER   I. 

SOURCES   OF   LIGHT. 

1.  NONE  of  our  senses  supplied  us  with  such  ex- 
tensive and  exact  knowledge  of  the  external  world  as 
that  of  sight.  The  eye  penetrates  into  the  unfathomable 
abysses  of  space,  and  receives  intelligence  from  regions 
the  most  remote  and  inaccessible  ;  it  reveals  to  us  the 
delicate  cells  of  which  living  beings  are  composed, 
and  perceives  the  animalcules  that  people  the  waters, 
whilst  the  manifold  forms  which  it  discloses  to  the 
mind  are  rivalled  only  by  the  exquisite  beauty  and 
charm  of  colour  with  which  the  physical  world  appears 
to  be  decorated. 

The  visual  organ,  like  every  other  special  sense, 
possesses  a  peculiar  form  of  sensibility,  that  of  per- 
ceiving luminous  rays,  a  faculty  which  admits  of  no 
more  precise  definition  and  explanation  than  the  cor- 
responding sensations  of  sound  or  heat,  of  taste  or  smell 

The  sensation  of  light  can  only  be  excited  in  our 
minds  by  a  stimulus  of  one  kind  or  another  acting  upon 
the  retina,  which  is  the  delicate  expansion  of  the  optic 
nerve  lining  the  posterior  part  of  the  eye-ball.  The 


2  OPTICS. 

stimulus  exciting  the  sensation  may  be  either  me- 
chanical, as  by  a  blow,  or  by  pressure  made  upon  the 
eye ;  or  electrical,  as  by  the  passing  of  a  current  of 
electricity  ;  or  it  may  even  be  produced  by  the  motion 
of  the  blood  in  the  vessels  of  the  retina  itself. 

External  objects  can  therefore  only  be  perceived  by 
our  eyes,  or  be  seen  by  us  as  the  result  of  something 
proceeding  from  them,  which  reaches  our  retina,  and 
stimulates  it  to  activity.  This  something  we  call  light. 

The  science  of  light  (optics)  has  a  twofold  problem 
to  solve.  On  the  one  hand  it  has  to  investigate  the 
laws  of  light,  and  on  the  other  to  enquire  into  the 
phenomena  of  vision.  The  former  constitutes  Physical 
Optics ;  the  latter,  Physiological  Optics.  The  former, 
or  physical  optics,  is  the  proper  subject  of  the  present 
course  of  lectures. 

2.  Every  form  of  matter  when  sufficiently  heated 
ha.s  the  power  of  emitting  rays  of  light,  and  thus  be- 
comes self-luminous.  This  condition  is  termed  incan- 
descence, and  the  self-luminous  worlds,  as  the  sun  a.nd 
fixed  stars,  are  doubtless  in  a  condition  of  intense  in- 
candescence. All  artificial  sources  of  light  depend  upon 
the  development  of  light  during  incandescence.  For 
the  illumination  of  our  streets  and  houses  at  night  we 
make  use  of  a  combustible  gaseous  combination  of 
carbon  and  hydrogen,  which  forms  the  chief  constituent 
of  ordinary  coal-gas.  When  this  hydrocarbon  burns, 
that  is  to  say,  when  its  elements  unite  with  the  oxygen 
of  the  air,  it  undergoes,  with  coincident  evolution  of 
heat,  partial  decomposition.  Carbon  is  separated  in 
the  solid  state,  and  floats  in  a  finely-divided  and  in- 
candescent state  in  the  interior  of  the  burning  vapour, 
and  this  constitutes  the  flame.  The  presence  of  theso 


SOURCES  OF  LIGHT.  3 

particles  of  carbon  may  be  easily  shown  by  holding  any 
non-combustible  body  in  the  flame,  when  the  carbon  in 
fine  powder  will  be  deposited  upon  it,  forming  a  layer 
of  soot.  The  combustion  of  the  particles  of  carbon 
takes  place  at  the  border  of  the  flame,  where  they  are 
first  brought  into  contact  with  the  oxygen  of  the  air ; 
but  if  the  supply  of  oxygen  to  them  be  insufficient  in 
quantity,  they  escape  in  a  partially  unburnt  condition  in 
the  form  of  a  dark  cloud;  and  the  flame  is  said  to  smoke. 
The  brightness  of  the  flame  is  owing  to  these  solid 
incandescent  particles,  for  the  burning  gas  itself  pos- 


FlG.  1. 


B  onsen's  burner. 

sesses  only  a  feeble  illuminating  power.  This  fact  may 
easily  be  demonstrated  by  means  of  a  Bunsen's  burner 
( fig.  1  ].  In  this  form  of  burner  ordinary  gas  conducted 
through  india-rubber  tubing  streams  into  the  tube  of 
the  burner.  Air  enters,  however,  through  an  opening 
(shown  in  the  adjoining  sketch),  as  well  as  through  a 


4  OPTICS. 

second  opening  opposite  to  it,  and  mixes  itself  with  the 
gas  in  the  interior  of  the  tube.  If  the  mixture  issuing 
from  the  tube  be  now  ignited,  it  burns  with  an  extremely 
feeble  flame  which  deposits  no  soot  on  bodies  held  in 
it.  For  now  oxygen  is  admitted  not  only  to  the  border 
of  the  flame,  but  throughout  its  whole  mass,  and  the  car- 
bon is  accordingly  burnt  into  carbonic  acid  before  it  can 
separate  in  the  solid  form,  so  that  the  flame  is  composed 
of  incandescpnt  gases  alone.  Its  illuminating  power  is 
therefore  very  feeble  ;  on  the  other  hand,  in  consequence 
of  the  more  perfect  combustion  that  takes  place  it 
possesses  a  far  higher  temperature  than  the  flame  of 
ordinary  gas.  It  is  used  a.s  a  heat-producing  flame,  and 
its  temperature  can  be  still  further  raised  by  a  short 
conical  chimney  supported  on  six  metal  arms  arranged 
in  the  form  of  a  star.  If  a  solid  body  be  introduced  into 
this  feebly-luminous  flame,  such,  for  instance,  as  a  piece 
of  platinum  wire  (see  the  figure),  the  incandescent  metal 
glows  with  a  brilliant  light.  The  luminosity  of  a 
Bunsen's  burner  can  be  restored  by  shutting  off  the 
entry  of  air,  either  by  closing  the  holes  with  the  linger 
or  by  the  rotation  of  a  slide  which  covers  them.  The 
light  then  becomes  much  more  brilliant,  with  abundant 
formation  of  smoke,  its  temperature  at  the  same  time 
falling  considerably. 

The  flames  of  candles  and  lamps,  whether  the  sub- 
stance burnt  be  tallow  or  wax,  rape-oil  or  petroleum, 
do  not  differ  essentially  from  that  of  an  ordinary  gas 
burner.  The  same  hydrocarbon  gas  which  constitutes 
the  essential  constituent  of  common  gas  is  burnt  also  in 
them.  The  hot  wick  which  draws  up  the  fluid  material 
about  to  be  burnt  plays  the  part  of  a  small  gas  factory, 
the  produce  of  which  is  used  on  the  spot.  The  flan;es 


SOUECES   OF  LIGHT.  5 

of  candles  and  of  lamps  all  owe  their  luminosity  to  the 
incandescence  of  particles  of  carbon  floating  in  them. 

3.  A  petroleum  lamp  burns,  in  the  first  instance, 
with  a  dull  murky  flame,  giving  off  a  large  quantity  of 
smoke,  but  it  acquires  a  high  degree  of  luminosity 
when  the  glass  chimney  is  applied,  for  the  pi^esence  of 
the  chimney  causes  a  strong  draught,  supplying  the  air 
requisite  for  the  thorough  combustion  of  the  gas  with 
which  it  was  previously  insufficiently  intermingled. 
The  brilliancy  of  a  petroleum  flame  is  thus  materially 
exalted  by  an  increased  supply  of  air,  whilst  that  of  a 
Bunsen's  burner,  as  has  just  been  seen,  is  almost 
abolished  by  the  same  means.  The  contrary  effects 
observed  in  these  two  cases  admit  of  easy  explanation. 
In  the  latter  instance  the  amount  of  air  supplied  is  so 
great  that  scarcely  any  of  that  separation  of  the  particles 
of  carbon  takes  place,  which  is  so  necessary  in  order  that 
a  bright  light  should  be  produced.  But  in  a  petroleum 
lamp,  the  introduction  of  a  moderate  quantity  of  air, 
by  effecting  the  combustion  of  the  superfluous  particles 
of  carbon,  causes  a  higher  degree  of  heat,  and  con- 
sequently a  more  lively  incandescence  and  illumination 
of  the  still  remaining  particles. 

From  all  this  it  is  obvious  that  in  order  to  obtain 
the  highest  illuminating  power  of  a  flame  in  which 
hydrocarbonaceous  compounds  are  undergoing  combus- 
tion, the  regulation  of  the  supply  of  air  is  essential. 
A  still  greater  degree  of  illumination  may  be  obtained, 
:f,  instead  of  air,  which  only  contains  one-fifth  of 
oxygen,  an  appropriate  quantity  of  pure  oxygen  is 
conducted  into  the  flame.  A  burner  constructed  with 
this  object  in  view  is  here  shown  (fig.  2,)  and  is  termed 
the  oxygen  lamp  or  burner.  In  this  burner  coal-gas 


6 


OPTICS. 


FIG.  2. 


Oxygen  lamp. 


1'iu. 


flows  through  the  upper  horizontal  tube  into  a  wide  one 
closed  below.  Through  the  middle  of  this  runs  a  second 
narrow  tube,  which  is  a  continuation 
of  the  lower  horizontal  one,  and  con- 
ducts oxygen  from  an  adjoining  gaso- 
meter. At  the  orifice  the  interspace 
between  the  two  tubes  is  closed  by 
a  funnel-shaped  plug,  perforated 
by  a  series  of  small  openings  from 
which  the  coal-gas  escapes.  When 
this  is  ignited  the  oxygen  is  turned 
on  and  enters  the  interior  of  the  flame,  the  proportion  of 
the  two  gases  being  regulated  by  means  of  two  stop- 
cocks, shown  in  the  figure. 
The  circular  flame  can 
thus  be  easily  rendered 
intolerably  bright. 

4.  If  more  oxygen  be 
admitted  than  is  necessary 
to  produce  the  greatest 
degree  of  illumination,  the 
brilliancy  of  the  flame  is 
diminished,  but  its  heat 
becomes  correspondingly 
increased  in  intensity.  If 
a  bundle  of  iron  wire  be 
held  in  the  flame  the  metal 
burns  with  vivacity,  giving 
off  beautiful  sparks  and 
Drummond's  light.  falling  in  molten  drops. 

On  the  other  hand,  if  an  infusible  and  incombustible 
substance,  as  chalk  or  magnesia,  be  introduced  into 
the  hot  flame,  it  is  raised  to  white  heat  and  emits 


SOURCES   OF  LIGHT.  7 

a  blinding  glare.  To  obtain  this — Drummond's  lime 
light,  as  it  has  been  named,  after  its  inventor — the 
arrangement  (shown  in  fig.  3),  may  be  conveniently 
used.  Its  construction  is  easily  intelligible  from  what 
has  been  previously  stated.  The  bent  burner,  shown 
separately  at  the  side,  consists  of  a  tube  traversed  by  a 
smaller  one,  which  last  conducts  oxygen  into  the  flame 
of  coal-gas  issuing  from  the  annular  intervening  space 
between  the  two  tubes.  The  obliquely  directed  flame 
plays  against  a  cylinder  of  magnesia  or  lime,  supported 
on  a  convenient  stand,  and  raises  it  to  a  white  heat.  The 
stop-cocks  serve  to  regulate  the  proportion  of  the  gases. 

5.  In  the  sources  of  lig^ht  that  have  hitherto  been 
considered  there  has   always  been  a  flame ;    that  is  to 
say,  a  stream  of  burning  gas,  by  the  heat  of  which   a 
solid  body  is  brought  to  incandescence  and  is  the  cause 
of  the  light.      In  the  Magnesium   Lamp,  of    which    a 
description  will  now  be  given,  a  solid  body,  magnesium, 
with  its  silvery  lustre,  is  burnt  in  the  open  air,  and  the 
solid    product   of    its    combustion,    magnesium    oxide 
(magnesia),  shines  with  a  splendid  light. 

The  construction  of  the  magnesium  lamp  made  by 
Salomon  and  Grant,  of  London,  is  represented  in  fig.  4. 
A  cylindrical  box,  6r,  contains  two  caoutchouc  rollers, 
which,  by  means  of  clockwork  set  in  motion  by  the  key 
c,  cause  a  coil  of  magnesium  wire,  on  the  wheel  K,  to 
be  slowly  unwound  and  passed  through  the  tube  Rf,  in 
proportion  to  the  rapidity  with  which  it  is  burnt  at  /. 
After  the  end  of  the  magnesium  wire  has  been  ignited, 
the  clockwork  is  set  in  motion  by  pressure  on  the  lever 
ra,  whilst  it  is  stopped  by  removing  the  pressure. 

6.  None  of  these  means  of  illumination,  however 
brilliant  are  those  of  the  lime  light  and  of  the  mag- 


8 


OPTICS. 


iiesium  lamp,  are  comparable  with  the  dazzling  light  of 
the  electric  current  passing  between  carbon  points, 
which  is  only  surpassed  by  the  light  of  the  sun  itself. 


FIG.  4. 


The  magnesium  lamp. 

The  apparatus  shown  in  fig.  5  may  be  used  for  the 
production  of  the  electric  light.  Two  metal  rods,  to  the 
extremities  of  which  pieces  of  hard  gas  coke  are  attached, 


FIG.  5. 


Electric  light  between  carbon  points. 


are  made  to  slide  through  tubes  supported  on  insulating 
glass  stands.  Each  rod  is  connected  by  a  wire  with  one 
pole  of  a  voltaic  battery  of  about  50  Bunsen's  cells.  If 


SOURCES   OF  LIGHT.  9 

the  carbon  points  are  brought  into  apposition  they 
become  intensely  incandescent  at  the  points  of  contact, 
and  they  can  then  be  withdrawn  for  some  distance  from 
each  other  without  interrupting  the  current  or  the  light 
it  produces. 

Between  the  carbon  points  an  arc  of  glowing  par- 
ticles of  carbon  appears,  the  so-called  Volta's  arc  of 
flame,  which  effects  the  conduction  of  the  current  at  the 
point  of  interruption.  This  nickering  arc  of  flame  is 
far  less  bright  than  the  carbon  points  themselves ;  the 
particles  of  carbon  of  which  it  is  composed  detach 
themselves  from  the  positive  pole,  which  is  the  hottest 
of  the  two,  and  fly  across  to  the  negative  pole.  As  a 
result  of  this,  after  a  short  time  the  positive  pole  be- 
comes shortened  and  even  excavated,  whilst  the  negative 
preserves  its  pointed  form.  At  the  same  time  combus- 
tion of  both  poles  takes  place  to  a  certain  extent, 
owing  to  the  action  of  the  atmospheric  air ;  and  the 
positive  pole,  which  is  exposed  to  the  destructive  action 
of  two  agents,  is  more  rapidly  consumed  than  the 
negative.  The  light-phenomena  are  as  brilliant  in 
vacuo  as  in  air ;  and  since  the  combustion  of  the  carbon 
is  thus  avoided,  the  positive  pole,  which  furnishes  the 
particles  of  carbon  for  the  arc  of  flame,  alone  wastes 
away.  This  experiment  shows  that  the  source  of  white 
heat  is  not  here  the  process  of  combustion,  as  in  the 
above-mentioned  cases,  but  results  from  the  glow 
produced  by  the  electrical  current. 

7.  The  resistance  which  the  current  has  to  overcome 
in  passing  from  one  carbon  point  to  the  other  is  greater 
in  proportion  as  the  distance  between  them  increases, 
owing  to  their  burning  away.  The  strength  of  tlxe 
current,  however,  correspondingly  diminishes,  till  it  is 


10  OPTICS. 

no  louger  capable  of  forming  an  incandescent  arc 
between  the  opposite  poles.  The  current  is  then  in- 
terrupted, and  the  light  dies  out.  Hence  if  practical 
use  is  to  be  made  of  the  electric  carbon  light,  it  is 
obvious  that  care  must  be  taken  to  keep  the  carbon 
points  always  at  a  proper  distance  from  each  other, 
and  for  this  purpose  apparatuses  have  been  invented 
which  automatically  approximate  the  points  in  propor- 
tion as  they  are  burnt  away,  and  these  have  been  named 
carbon-light  regulators  or  electric  lamps. 

The  Regulator  of  Foucault  and  Dubosq,  the  con- 
struction of  which  is  shown  in  fig.  ti,  is  a  master- 
piece of  ingenuity  and  mechanical  adaptation.  A  com- 
plete account  of  this  complicated  machine  would 
here  be  out  of  place.  It  will  be  sufficient  to  say  that 
by  means  of  clockwork  the  two  carbon  points  are  made 
to  approximate  to  each  other,  the  inferior  (positive) 
pole  moving  rather  faster  than  the  other,  in  view  of  the 
greater  rapidity  with  which  it  is  burnt  off.  Before  the 
current  reaches  this  it  circulates  round  the  coil  of  an 
electro-magnet;  as  long  as  the  carbon  points  preserve 
their  proper  distance  from  each  other  the  electro- magnet 
is  sufficiently  strongly  magnetised  to  fix  an  iron  detent, 
a.nd  thus  to  check  the  clockwork.  As  soon,  however, 
as  the  distance  between  the  carbon  points,  in  conse- 
quence of  combustion,  becomes  greater,  the  strength  of 
the  current  diminishes  and  the  electro-magnet  is  ren- 
dered less  powerful — the  detent  is  accordingly  set  free, 
the  clockwork  acts,  and  the  carbon  points  approximate, 
which  again  re-establishes  the  current  in  its  former 
intensity ;  the  keeper  is  then  again  attracted  and  the 
clockwork  checked  anew.  By  means  of  the  automatic 
action  of  the  Regulator,  not  only  are  the  carbon  points 


SOURCES  OF  LIGHT. 


11 


kept  at  a  constant  and  equal  distance  from  each  other, 
but  the  arc  of  flame  can  be  maintained  unbroken  for 
hours  together  in  the  same  place. 

FIG.  6. 


Electric  lamp. 

8.  All  bodies  that  do  not  themselves  produce  light 
can  only  be  seen  by  means  of  the  light  they  receive  and 


12  OPTICS. 

reflect  to  our  eyes  from  self-lnminous  bodies.  Amorist 
the  heavenly  bodies,  the  moon  and  planets  are  in  this 
case,  for  they  are  illuminated  by  the  sun,  as  are  most 
terrestrial  objects.  The  light  falling  upon  such  non- 
luminous  bodies  is  diffusely  reflected  from  their  surface ; 
that  is  to  say,  in  such  a  manner  that  every  illuminated 
point  throws  out  rays  from  the  surface  in  every 
direction. 

Every  illuminated  body,  reflecting  light  diffusely,  plays 
the  part  of  a  source  of  light.  It  shines  with  borrowed 
light.  Our  earth,  like  the  moon  and  planets,  is  in  this 
position,  in  comparison  with  the  self-lurninous  stars. 
The  faint  light  which  the  new  moon  presents,  and  which 
makes  tha.t  part  of  her  disk  visible  which  is  not  directly 
LI  laminated  by  the  sun,  is  only  the  reflection  of  the  earth 
illuminated  by  the  sun's  rays. 

0.  Light,  proceeding  from  a  self-luminous  or  from 
an  illuminated  object,  must  traverse  the  humours  of 
the  eye  before  producing  a  sensa/fcion  in  us  by  exciting 
the  retina.  Bodies  which,  like  the  contents  of  the 
globe  of  the  eye,  or  like  air,  water,  glass,  etc.,  permit 
light  to  pass  through  them,  are  called  transparent ;  on 
the  other  hand,  those  which  transmit  no  light  are  said 
to  be  opaque.  This  difference,  however  sharply  ex- 
pressed it  may  usually  appear  to  be,  is  not  due  to  any 
absolute  difference,  for  every  opaque  body  if  reduced 
to  a  sufficiently  thin  film  becomes  transparent,  whilst 
transparent  bodies  permit  the  passage  of  less  light  in 
proportion  to  their  thickness.  In  the  abyss  of  the  sea 
the  darkness  of  night  prevails,  because  only  a  sparing 
amount  of  light  is  capable  of  traversing  a  mile  or  more 
of  water.  On  the  other  hand,  the  most  opaque  bodies, 
like  the  metals,  can  be  rendered  so  thin  that  a  subdued 


SOURChS  OF  LIGHT. 


light  glimmers  through  them.  Foucault  has,  in  fact, 
proposed  to  cover  the  object-glass  of  a  telescope  in- 
tended for  solar  observation  with  a  thin  precipitate  of 
silver,  in  order  to  protect  the  eye  of  the  observer  from 
thf  glare,  without  loss  of  definition. 


OPTICS. 


CHAPTER  II. 

RECTILINEAR  PROPAGATION    OP    JJGHT. 

10.  AN  opaque  body  is  illuminated  on  that  side  of 
its  surface  only  which  is  turned  towards  the  light,  its 
opposite  surface,  as  well  as  a  space  covered  by  it,  the 
shadow,  remains  dark.  The  shadow  of  a  body  is  pro- 
jected upon  a  plane  surface  held  in  the  shadow-space 
as  a  similarly  formed  dark  spot,  which  occupies  that 
part  of  the  plane  to  which  the  access  of  light  is  pre- 
vented by  the  body  throwing  the  shadow.  It  may 
easily  be  demonstrated  that  all  straight  lines  conceived 
to  be  drawn  from  any  point  of  the  shadow  thrown  upon 
the  plane  to  the  source  of  light,  strike  against  the 
opaque  body,  and  that  only  those  points  of  the  plane 
receive  light  which  are  so  placed  that  straight  lines 
drawn  to  them  from  the  source  of  light  are  not  arrested 
by  the  shadow-giving  body. 

From  these  facts  the  conclusion  may  be  drawn 
that  light  proceeding  from  a  luminous  body  whilst  tra- 
versing a  homogeneous  medium  is  propagated  in  every 
direction  in  straight  lines,  which  are  called  rays  of  light. 
Those  rays  which  we  may  conceive  to  be  drawn  from 
the  luminous  pcint  s  (fig.  7),  to  the  circumference  of 
the  shadow,  graze  the  surface  of  the  body  throwing  the 
shadow  and  collectively  form  a  cone  which  invests  the 
body  like  a  ring.  The  line  formed  by  all  the  points  of 


RECTILINEAR  PROPAGATION   OF  LIGHT.  15 

contact  is  the  limit  between  the  front  illuminated  and 
the  back  un illuminated  surface  of  the  body.  The 
shadow  which  the  object  throws  upon  any  plane  or 
curved  surface  is  nothing  but  the  section _of^this  cone 

FIG.  7. 


Shadows. 

of  contact-lines  by  the  plane  in  question.  It  conse- 
quently holds  a  direct  geometric  relation  to  the  form 
of  the  object,  and  forms  a  simple  outline  image  of  it 
or  silhouette.  Shadows  supply  to  our  eyes,  which  as 
it  were  unconsciously  follow  the  geometric  relation 
between  the  form  of  the  shadow  and  that  of  the  object, 
valuable  means  for  the  correct  judgment  of  the  real 
form  of  bodies  in  space.  The  painter  uses  them  to 
make  his  figures  stand  out  from  the  canvas.  In  tech- 
nical drawings  of  machines,  scaffolding,  etc.,  which  are 
to  serve  as  plans  for  the  artificer,  in  addition  to  the 
elevation  there  must  always  be  a  'ground  plan,'  in 
order  that  the  perspective  relations  of  the  building  may 
be  understood.  But  if  in  the  former  the  strictly  geo- 
metric shadows  were  given,  the  second  might  in  many 
cases  be  dispensed  with. 

11.  If  the  body  casting  a  shadow  be  illuminated,, 
not  by  a  single  luminous  point,  as  has  been  supposed  in 
the  foregoing  illustrations,  but  by  a  bright  body  which 
possesses  innumerable  luminous  points,  we  must,  in 
order  to  know  the  nature  of  the  shadow,  imagine  a 
shadow  cone  for  eaoh  luminous  point ;  the  space  behind 
the  opaque  body  which  is  common  to  all  these  cones 
receives  no  rays  from  the  luminous  body  and  is  termed  the 


16  OPTICS. 

nucleus  of  the  shadow  ;  but  this  is  surrounded  by  a  space 
which  is  only  in  shadow  as  regards  a  part  of  the  luminous 
body,  whilst  it  receives  light  from  the  rest  of  it  and  is 
consequently  partially  illuminated.  It  is  termed  the  half 
shadow  or  penumbra.  Fig.  8  shows  the  case  of  a  large 
luminous  sphere,  A,  opposite  which  is  a  smaller  opaque 
one,  B  ;  the  simple  construction  shows  what  determines 


FIG.  8  arid  FIG.  9. 


• 


Shadow  nucleus,  and  penumbra. 


the  limits  of  the  nucleus  of  the  shadow  and  the  pe- 
numbra. The  conical  nucleus  of  the  shadow  terminates 
in  a  point  at  S,  whilst  the  penumbra  stretches  away 
constantly  widening  to  infinity.  A  plane  held  in  the 
shadow  at  m  n,  perpendicular  to  the  axis  of  the  cone, 
receives  the  image  represented  in  fig.  9,  where  a  central 
dark  spot  is  seen  corresponding  to  the  nucleus  of  the 
shadow,  and  is  surrounded  by  a  less  dark  area,  the  shade 
of  which  gradually  diminishes  from  within  outwards  till 
it  is  no  longer  perceptible.  If  the  plane  be  closely 
approximated  to  the  body  giving  the  shadow,  the  broad 
dark  nuclear  shadow  loses  but  little  of  its  definition, 
the  half  shadow  surrounding  it  appearing  only  as  a 
narrow  border.  If  placed  at  a  greater  distance,  the 
penumbra  exceeds  the  nucleus  of  the  shadow  in  breadth, 
and  only  an  ill-defined  shadow  results.  An  explanation 
is  thus  afforded  why  we  are  unable  to  point  out  the 


RECTILINEAR  PROPAGATION   OF  LIGHT.  17 

exact  spot  where  the  shadow  of  a  steeple  ends  on  the 
ground.  So  if  a  knitting-needle  be  held  in  the  sun 
immediately  in  front  of  a  sheet  of  paper,  it  throws  a  very 
well-defined  shadow ;  but  if  it  be  removed  to  a  distance 
of  only  three  or  four  inches  from  the  sheet  no  accurate 
outline  can  be  traced  of  its  ill-defined  shadow. 

Our  planetary  system  affords  striking  illustrations 
of  such  shadow  cones  as  are  shown  in  fig.  8.  The 
shadow  nucleus  behind  the  moon  is  nearly  equal  to  the 
radius  of  the  moon's  orbit,  and  can,  therefore,  when  the 
moon  intervenes  between  the  sun  and  the  earth,  which 
is  only  possible  at  the  time  of  the  new  moon,  reach  the 
surface  of  the  earth.  The  sun  is  then  totally  covered 
by  the  moon,  or  there  is  said  to  be  a  total  eclipse  of  the 
mn  over  those  parts  of  the  earth  which  are  in  the 
nuclear  shadow ;  whilst  in  those  parts  which  lie  in  the 
penumbra  a  sickle-shaped  portion  of  the  sun's  disk 
remains  visible,  and  the  eclipse  is  only  a  partial  one. 

The  nuclear  shadow  of  the  earth  extends  behind  it 
to  a  distance  of  216  of  its  semidiameters,  and  thus 
reaches  far  beyond  the  radius  of  the  moon's  orbit, 
which  amounts  to  only  60  semidiameters  of  the  earth. 
At  the  time  of  the  full  moon  it  may  happen  that  the 
moon  lies  wholly  or  partially  in  the  earth's  shadow,  and 
the  interesting  spectacle  of  a  lunar  eclipse  is  presented 
to  us. 

12.  To  an  observer  placed  at  the  point  8  of  the  cone 
(fig.  8),  the  smaller  but  nearer  sphere  B  appears  to  be 
of  exactly  the  same  size  as  the  larger  but  more  remote 
sphere  A,  the  latter  being  precisely  covered  by  the 
former.  The  apparent  size  of  an  object  is  determined 
by  the  angle  which  the  rays  of  light,  passing  from  its 
outermost  points  to  the  eye,  form  with  one  another, 


18  OPTICS. 

fche  so-called  visual  angle.  The  same  body  is  seen 
under  a  smaller  visual  angle,  and  of  correspondingly 
smaller  size  the  further  it  is  removed  from  our  eyes, 
and  two  bodies  of  different  size  appear  under  the  same 
visual  angle  if  their  distances  are  inversely  as  theii 
diameter.  If  we  are  acquainted  with  the  real  size  of 
an  object  we  can  determine  its  distance  from  us  by 
the  visual  angle  under  which  it  appears  to  us ;  and,  vice 
vjrsd,  if  the  distance  and  the  apparent  size  be  given,  we 
can  determine  its  actual  size.  Astronomers  employ 
these  si  in  9e  data  to  determine  the  size  and  distance  of 
the  heavenly  bodies.  It  has  been  found,  for  example, 
by  appropriate  observations,  that  the  semidiameter  of 
the  earth,  seen  from  the  sun,  would  appear  under  a 
visual  angle  of  only  8'  6".  This  is  termed  the  parallax 
of  the  sun ;  and  from  thence  the  calculation  has  been 
made  that  the  distance  of  the  earth  from  the  sun 
amounts  to  24,000  seniidiameters  of  the  earth,  and  after 
this  distance  is  determined  it  results,  from  the  visual 
angle  of  32'  under  which  the  sun  appears  to  us,  that  its 
diameter  is  112  times  greater  than  that  of  the  earth. 

The  same  operations  by  which  the  astronomer  ob- 
tains his  results  school  us  from  our  youth  upwards  to 
form  every  day  and  every  hour  an  unconscious  estimate 
of  the  size  and  distance  of  terrestrial  objects  by  the 
measurement  of  the  eye.  The  visual  angle  under  which 
a  human  form  or  other  object  of  known  size  appears  to 
us  supplies  us  with  a  datum  from  which  we  estimate 
its  distance,  and  this  distance  again  enables  us  to  form 
a  judgment  in  respect  to  the  size  of  neighbouring 
objects.  .The  rays  of  light  which  reach,  the  microscopi- 
cally small  earth  from  the  various  parts  of  the  mighty 
mass  of  the  sun,  do  not  form  a  greater  angle  with 


EKCTILINEAR  PROPAGATION   OF   LIGHT,  19 

each  other  at  most  than  '32',  which  expresses  the  ap- 
parent size  of  the  sun,  and  may  therefore  be  regarded 
as  being  almost  parallel.  If  a  beam  of  the  sun's  rays 
be  allowed  to  enter  a  chamber  through  a  wide  opening 
in  the  window  shutter,  it  may  be  easily  followed  by  the 
illumination  of  the  floating  particles  of  dust,  and  it  ma} 
be  shown  that  it  has  everywhere  the  same  diameter, 
and  must  consequently  be  composed  of  parallel  rays. 

13.  If  now  the  chamber  be  completely  darkened, 
and  a  very  small  opening  of  from  1-3  millimetres 
(-j'g-th— |th  of  an  inch)  be  made  in  the  shutter,  a  very 
pretty  appearance  may  be  observed  upon  a  paper  screen 
placed  opposite  to  the  opening.  The  neighbouring 
buildings  are  seen  with  their  roofs,  chimriies,  and 
windows  ;  the  green  tree  tops  waving  in  the  wind,  men 
walking  in  the  streets,  white  clouds  sailing  over  the 
blue  sky,  in  fact  a  complete  picture  of  the  external 
world  is  as  it  were  painted  in  delicate  colours  upon  the 
screen.  But  this  picture  is  inverted ;  what  is  in  reality 
above  appears  in  the  picture  below,  what  is  there  on  the 
left  is  here  on  the  right,  and  vice  versa.  When  the  screen 
is  brought  nearer  to  the  opening,  the  picture  becomes 
smaller  but  clearer ;  when  it  is  removed  to  a  greater  dis- 
tance it  becomes  fainter  but  its  size  is  increased.  If 
the  circular  opening  be  replaced  by  a  square  one  of  equal 
area,  the  picture  undergoes  no  change,  nor  does  any 
alteration  occur  if  the  square  be  changed  to  a  triangle 
of  equal  area ;  but  when,  on  the  other  hand,  a  series 
of  continuously  larger  and  larger  openings  be  used,  the 
picture  will  be  found  to  become  progressively  brighter, 
whilst  its  outline  becomes  more  and  more  confused  and 
blurred,  until,  when -the  opening  is  several  centimetres 


20 


OPTICS. 


in  diameter,  no  definite  picture  can  be  discerned  upon 
the  screen,  but  only  a  uniformly  illuminated  surface. 

The  mode  of  production  of  this  charming  picture  is 
best  explained  by  a  repetition  of  the  same  experiment 
in  a  simpler  form.  A  lighted  candle  is  placed  in  front 
of  a  screen  perforated  by  a  small  opening  (0,  fig.  10), 
and  behind  it  a  white  paper  screen  (8)  is  held  which 
receives  the  inverted  imasre  of  the  flame. 


Amongst  the 


FIG.  10. 


Projection  of  an.  image  through  a  small  aperture. 

innumerable  rays  of  light  which,  for  example,  the  high- 
est point,  Ay  of  the  flame  emits,  only  a  small  conical 
fasciculus  (A  a)  traverses  the  aperture  and  forms  upon 
the  screen  a  small  bright  spot  (a)  which,  in  conse- 
quence of  the  rectilinear  course  of  the  rays  of  light  is 
only  illuminated  with  the  light  of  the  point  A,  whilst  no 
other  part  of  the  screen  can  receive  light  from  this 
point.  In  the  same  way,  the  spot  6,  situated  upon  a 
higher  part  of  the  screen,  is  only  illuminated  by  the 
lower  point,  B,  of  the  object.  Now  since  every  point 
of  the  object  sends  its  luminous  rays  separately  to 
different  points  of  the  screen,  the  continuous  serial 
addition  of  innumerable  bright  spots  forms  an  image 


RECTILINEAR  PROPAGATION   OF   LIGHT.  21 

which,  as  is  immediately  intelligible  from  the  figure, 
resembles  the  object,  and  is  larger  in  proportion  as  the 
screen  is  removed  from  the  aperture.  The  larger  the 
image,  the  feebler  is  its  illumination,  because  the  same 
quantity  of  light  is  then  distributed  over  a  larger 
surface. 

The  small  spot  of  light,  a,  must  necessarily  be  cir- 
cular or  square  or  triangular,  in  accordance  with  the 
shape  of  the  opening.  But  since  the  adjoining  light 
spots  overlap  each  other,  its  particular  form  is  of  no 
importance ;  and  the  result  is  the  same  in  regard  to 
the  entire  image,  whatever  may  be  the  form  of  the 
aperture.  If  the  rays  of  the  sun  penetrate  through  a 
partially  closed  window  shutter  they  throw  upon  the 
floor  of  the  room  bright  elongated  and  rounded  spots 
of  light.  These  are  so  many  images  of  the  sun's  disk 
thrown  by  the  various  irregularly  formed  chinks  and 
apertures  of  the  shutter.  The  illuminated  spots  do 
not  appear  circular  but  elliptical,  because  the  surface 
of  the  floor  on  which  they  fall  is  not  perpendicular  to 
the  direction  of  the  sun's  rays.  The  spaces  between 
the  leaves  of  the  thick  foliage  of  a  tree  act  in  the  same 
way,  and  produce  numerous  elliptical  images  of  the  sun 
on  the  shaded  floor  of  the  forest.  In  partial  eclipse  of 
the  sun  these  light-spots  in  the  shadow  thrown  by 
trees  assume  a  distinctly  sickle-shaped  form. 

It  is  now  obvious  why  small  openings  are  alone 
capable  of  forming  such  images,  for  they  only  are 
capable  of  effecting  such  a  division  of  the  rays  of  light 
as  is  essential  for  the  production  of  an  image  :  large 
openings,  which  allow  rays  of  light  to  fall  upon  the 
screen  from  all  or  very  many  points  of  the  object,  are 
not  appropriate  for  the  purpose. 


22 


OPTICS. 


14.  If  there  be  a  luminous  point  at  L  (fig.  11),  and 
a,  by  c,  d  be  an  opaque  screen,  A,  B,  C,  D  would  be  the 
shadow  which  this  screen  would  throw  on  a  -second 
screen  placed  parallel  to  it.  If  the  second  screen  be 
just  twice  as  distant  from  the  source  of  light  as  the 
first,  the  area  of  the  shadow^will  be  four  times  as  large 
a?  the  screen  which  throws  the  shadow.  If  the  latter 
be  removed,  the  same  number  of  rays,  which  was  pre- 
viously received  by  it  and  illuminated  its  surface,  is 
now  distributed  over  an  area  of  four  times  the  size ;  a 

FIG.  11. 


Diminution  of  the  illumination  in  the  ratio  of  the  square  of  the  distance. 

given  portion  of  the  surface  A,  B,  C,  D,  receives,  con- 
sequently, four  times  less  light  than  a  corresponding 
portion  of  the  surface  a,  6,  c,  d,  and  will  be  therefore 
proportionately  less  strongly  illuminated.  The  source 
of  light  thus  gives,  at  double  the  distance,  only  the 
fourth  part  of  the  illumination  which  it  can  give  at 
unity.  If  the  second  screen  be  at  3,  4,  5  .  .  .  times  the 
distance  of  the  first  from  the  source  of  light,  the  shadow 
falling  upon  it  will  be  9,  16,  25  .  .  .  times  larger  than 
the  shadow-throwing  screen,  and  will,  according  to  its 


RECTILINEAR  PROPAGATION   OF   LIGHT. 


23 


distance,  be  9,  16,  25  ...  times  less  brilliantly  illumi- 
nated. 

We  thus  acquire  a  knowledge  of  the  law,  that  the 
amount  of  illumination  diminishes  in  proportion  to  the 
square  of  the  distance  from  the  source  of  illumination. 

The  apparatus  shown  in  fig.  12  may  be  employed 
to  demonstrate  the  truth  of  this  law  by  experiment.  A 
sheet  of  white  paper  is  stretched  on  a  frame,  supported 
on  a  stand  8,  in  the  centre  of  which  is  a  spot  of  oil, 
made  with  stearine.  The  grease  spot  allows  more 
light  to  pass  through  it,  and  consequently  reflects  less 

Fiu. 12. 


Bunsen's  Photometer. 

than  the  unstained  part  of  the  paper.  If  therefore 
the  paper  be  illuminated  more  strongly  from  behind, 
it  appears  bright  on  a  dark  ground.  On  the  other 
hand,  it  appears  dark  upon  a  bright  ground  if  it  be  more 
strongly  illuminated  on  the  front  surface  ;  whilst,  with 
equal  illumination  on  both  sides,  the  spot  becomes 
invisible,  since  it  can  then  appear  neither  darker  nor 
lighter  than  the  adjoining  paper.  The  flame  of  a 
candle,  a,  is  now  placed  upon  one  side  of  the  screen, 
whilst  four  such  flames  are  placed  upon  the  other  side 


24 


OPTICS. 


at  6,  and  the  screen  is  removed  to  such  a  distance  from 
them  that  the  spot  is  no  longer  visible.  This  will  be 
found  to  occur  when  the  distance  of  the  quadruple  flame 
from  the  screen  on  the  one  side  is  double  that  of  the 
single  flame  on  the  other  side.  This  experiment,  in 
which  a  source  of  light  four  times  as  strong  as  another 
gives  the  same  illumination  at  double  the  distance, 
corroborates  the  law  above  laid  down. 

This  law  being  admitted,  the  same  apparatus,  fig. 
12,  may  be  employed  as  a  means  of  comparing  the 
brilliancy  of  two  sources  of  light.  If,  for  example,  the 
flame  of  a  candle  be  placed  in  front  and  a  gas  flame 
behind  a  paper  screen,  and  this  be  moved  till  the  grease 

FIG.  13. 


Rumford's  Photometer. 

spot  disappears,  the  illuminating  power  of  the  two 
lights  will  be  as  the  squares  of  their  distances  from  the 
screen.  The  apparatus  employed  for  the  determination 
of  the  illuminating  powers  of  different  sources  of  light, 
are  termed  Photometers.  The  paper  screen  with  the 
grease  spot  constitutes  the  essential  feature  of  the 
Photometer  of  Bunsen. 

Rumford's  Photometer  is  of  remarkably  simple 
construction  (fig.  13).  An  opaque  rod,  about  the  size 
of  a  lead  pencil,  stands  in  front  of  a  white  paper  screen. 


KECTILINEAR  PROPAGATION   OF  LIGHT.  ^ 

The  two  lights  to  be  compared  both  cause  a  shadow  of 
the  pencil,  and  each  light  illuminates  the  shadow  cast 
by  the  other.  If  either  light  is  removed  to  such  a 
distance  that  the  two  shadows  appear  of  equal  depth, 
the  brilliancy  of  the  two  lights  will  be  as  the  squares  of 
their  distances  from  the  screen. 


26  OPTICS. 


CHAPTER  III. 

REFLEXION    OF    LIGHT. 

15.  IF  a  beam  of  parallel  rays  of  light  from  the  sun 
be  allowed  to  pass  obliquely  through  an  opening  in  the 
window  shutter  (fn,  fig.  14)  and 
to  fall  upon  the  plane  surface  of 
mercury  at  rest  (s  s'),  it  will  be  seen 
that  from  the  point  (n)  where  the 
beam  strikes  the    surface   of  the 
mercury,    a     second   fasciculus    of 
of  ligiit.  rajs  (n  d)  proceeds,  the  course  of 

which    may   be   followed    just    as 

easily  as  that  of  the  incident  ray,  by  its  illuminating 
the  floating  particles  in  the  air. 

This  process  is  termed  regular  reflexion,  in  opposition 
to  diffuse  reflexion,  which  has  been  already  referred  to 
(p.  12).  If  a  sheet  of  paper  be  placed  upon  the  mercury, 
the  reflected  beam  vanishes,  but  the  spot,  n,  where  the 
paper  is  struck  by  the  incident  rays  is  brilliantly  illu- 
minated and  becomes  visible  from  every  side  as  though 
it  were  self-luminous.  The  dull  surface  of  the  paper, 
although  it  may  be  struck  in  a  certain  direction  only  by 
rays  of  light,  thus  emits  rays  in  all  directions,  and  be- 
comes in  virtue  of  this  diffuse  reflexion  every  where  visible 
as  an  illuminated  object.  The  smooth  surface  of  the  mer- 
cury, on  the  other  hand,  appears  not  at  all  or  but  very 


REFLEXION   OF  LIGHT.  27 

feebly  illuminated  at  the  point  n  where  it  is  struck  by 
die  incident  rays  ;  it  reflects  them  in  a  perfectly  definite 
direction  without  otherwise  materially  altering  them. 
In  fact,  if  a  sufficiently  small  opening  be  made  in  the 
shutter,  the  same  oval  image  of  the  sun  appears  on  the 
roof  of  the  room  where  the  reflected  ray  falls,  as  the 
incident  ray  itself  would  have  formed  had  it  been  allowed 
to  fall  upon  the  floor. 

Every  smooth  surface  is  called  a  mirror,  and  Nature 
herself  offers  to  us,  in  the  surface  of  fluids  at  rest,  a 
very  perfect  example  of  a  mirror.  Mirrors,  however, 
that  are  composed  of  some  solid  material,  as  of  polished 
metal,  although  this  can  never  be  made  to  attain  the 
absolute  smoothness  of  the  surface  of  a  fluid,  are  very 
much  more  convenient  for  use.  The  kind  of  mirror 
most  commonly  employed  consists  of  a  plate  of  glass 
which  has  been  ground  and  polished  and  covered  on  one 
surface  with  an  amalgam  of  tin,  or  with  a  precipitate  of 
silver,  and  the  surface  of  the  metal  adhering  to  the  glass 
is  generally  the  reflecting  surface. 

In  order  to  indicate  accurately  the  course  of  the 
incident  and  reflected  rays,  we  must  conceive  a  vertical 
line,  or  perpendicular  (np),  to  fall  on  the  reflecting  sur- 
face at  the  point  n  (fig.  1-1)  where  it  is  struck  by  the 
incident  ray.  The  plane  drawn  through  the  incident 
ray  and  the  perpendicular,  which  is  itself  vertical  to 
the  plane  of  the  mirror,  is  called  the  plane  of  incidence  ; 
it  is  also  named  the  plane  of  reflexion,  because  it  always 
contains  the  reflected  ray.  The  path  pursued  by  the 
incident  and  the  reflected  rays  is  determined  by  the 
angle  of  incidence,  i,  and  the  angle  of  reflexion,  r,  which 
each  of  the  rays  make  with  the  perpendicular.  The 
angle  of  reflexion  is  always  equal  to  the  angle  of  incidence. 


28  OPTICS. 

These  two  propositions — that  the  planes  of  incidence 
and  reflexion  are  coincident,  and  that  the  angles  of  inci- 
dence and  reflexion  are  equal — together  constitute  the 
no  less  simple  than  important  law  of  the  reflexion  of  light. 
In  order  to  demonstrate  it  by  experiment,  the  instrument 
shown  in  fig.  15  may  be  used.  To  the  curved  border 
of  a  semicircular  piece  of  wood,  A  A,  a  plate  of  metal 
is  attached  which  has  a  vertical  slit  at  the  centre  of  its 
curve  (a),  and  from  this  point  outward  is  divided  into 
90°.  The  mirror/,  the  back  of  which  is  shown  in  the 
figure,  is  capable  of  being  rotated  round  a  vertical  axis, 

FIG.  15. 


A 

Model  for  the  demonstration  of  the  law  of  reflexion  of  light. 

B,  pas-sing  through  the  centre  of  the  semicircle.  The  rod 
6,  which  is  attached  to  the  mirror  and  points  by  means  of 
an  indicator,  c,  to  the  scale  of  degrees,  is  at  right  angles 
to  the  plane  of  the  mirror,  and  consequently  represents 
the  perpendicular.  If  now  a  small  beam  of  parallel 
rays  be  allowed  to  pass  through  the  slit  and  fall  on  the 
mirror,  the  reflexion  will  illuminate  and  make  visible 
that  part  of  the  circumference  of  the  circle  towards 
which  it  is  directed.  The  indicator  c  now  stands,  we 
will  say,  at  20°.  The  ray  coursing  from  a  to  /  strikes 
the  mirror  under  an  angle  of  incidence  of  20°,  and  hence  if 
the  above  law  of  reflexion  be  correct,  should  be  reflected 
to  the  line  marking  40°,  and  in  point  of  fact  it  will  be 


REFLEXION   OF   LIGHT. 


29 


found  that  this  is  the  degree  which  is  brilliantly  illumi- 
nated by  the  reflected  light.  If  now  the  indicator  be 
successively  placed  opposite  the  lines  marking  10°,  20°, 
30°,  etc.,  the  reflected  ray  will  successively  illuminate  the 
lines  marking  20°,  40°,  60°,  etc.,  as  the  law  of  reflexion 
requires  that  it  should  do.  If,  lastly,  the  indicator 
be  placed  opposite  the  slit  itself,  so  that  the  angle  of 
incidence  is  zero,  the  angle  of  reflexion  must  also  be 
zero;  the  reflected  ray  passes  out  again  by  the  slit  in 
the  same  direction  as  the  incident  ray  entered,  or  in 
other  words,  a  ray  of  light  falling  perpendicularly  upon 
a  mirror  is  reflected  upon  itself. 

16.  A  plxne  mirror  reflects   the   images  of  objects 


FTG  1C. 


Production  of  the  image  point  in  a  plane  mirror. 

placed  in  front  of  it,  ourselves  included,  with  an  accuracy 
that  is  proverbial.  The  production  of  these  images 
may  be  explained  in  the  simplest  manner  by  the  law  of 
reflexion.  In  the  diagram  (fig.  16}  An  and  A  p 
represent  two  out  of  the  innumerable  rays  which 
a  luminous  point  A  throws  upon  a  mirror  s Y.  If  we 
conceive  the  reflected  rays,  n  o,  p,  q,  corresponding  to 
them,  and  the  direction  of  which,  in  accordance  with 
the  above  law  admits  of  being  easily  ascertained,  to  be 
prolonged  backwards,  they  will  meet  each  other  in  the 


OPTICS. 


point  a.  The  straight  line  A  a,  which  joins  the  point  a 
with  the  luminous  point  A,  is  perpendicular  to  the  plane 
of  the  mirror  and  is  bisected  by  it  at  the  point  r,  that 
is  to  say,  a  r  —  A  r,  which  is  deducible  also  from  the 
fact  that  the  triangles  Anr  and  anr  are  equal  to  one 
another.  Since  any  pair  of  rays,  that  may  have  been 
selected  for  consideration,  pass  to  the  same  point,  a,  it 
follows  that  all  the  rays  proceeding  from  A  that  fall 
upon  the  mirror  can  similarly  be  carried  back  as  though 
they  proceeded  from  the  single  point  a.  We  can  there- 
fore make  the  following  proposition  as  a  direct  corollary 
of  the  law  of  reflexion  :— 

All  rays  that  proceed  from  a  luminous  point  and  fall 
upon  a  plane  mirror,  are  reflected  from  it  as  if  they  came 
from  a  point  in  a  perpendicular  dropped  from  the  luminous 
point  to  the  mirror,  as  far  behind  the  reflecting  surface  as 
this  is  in  front  of  it. 

An  observer  placed  in  front  of  the  mirror  receives 
consequently  the  reflected  rays 
as  if  the  point  a,  from  which 
they  appear  to  proceed,  were 
itself  the  luminous  point.  It 
sees  in,  that  is  to  say,  behind 
the  mirror,  the  point  a  as  the 
image  of  the  luminous  point  A, 
situated  in  front  of  the  mirror. 

In  the  same  way  an  image 
point  behind  the  mirror  cor- 
responds to  each  point  of  every 
luminous  or  illuminated  object, 
and  out  of  the  totality  of  the 

image-points  the  complete  mirror  image  or  reflexion  of 
the  object  is  produced.  In  order  to  conceive  this  image 


Fia.  17. 


Production  of  the  image  in  a 
mirror. 


REFLEXION   OF  LIGHT. 


31 


in  the  mind,  or  to  show  it  in  a  drawing  (fig-  17),  a  perpen- 
dicular must  be  conceived  to  be  struck  from  each  point 
of  the  object  to  the  plane  of  the  mirror,  and  prolonged 
as  far  behind  it  as  these  points  are  in  front  of  it.  In 
such  a  simple  object  as  an  arrow,  A  B  ( fig.  1  7),  which  may 
be  selected  as  an  example,  it  is  only  requisite  to  show 
the  construction  for  its  terminal  points,  A  and  I?,  by 
which  its  image  a  b  is  formed.  An  observer  situated  at 
o  receives  the  rays  from  the  point  of  the  arrow  in  the 
direction  A  n  o  and  from  the  other  extremity  in  the 
direction  B  p  o.  Simple  inspection  of  the  figure  shows 
that  the  image  and  the  object  must  be  of  equal  size, 
and  must  also  lie  symmetrically  with  regard  to  the 
plane  of  the  mirror. 

17.  The  polished  surface  of  this  plate  of  glass  (fig.  18) 


Fia. 18. 


Mirror- image  in  a  transparent  plate  of  glass. 

acts  as  a  mirror,  whilst  at  the  same  time  it  permits 
the  objects  behind  it  to  be  seen.  If  a  lighted  candle  be 
placed  on  one  side  the  image  is  reflected.  If  a  water 

•*>  O 

carafe  filled  with  wa.ter  be  placed  behind  the  glass  plate 
in  the  apparent  position  of  the  image,  the  illusory  im- 
pression is  produced  of  a  candle  burning  whilst  sub- 


32  OPTICS. 

merged  in  the  interior  of  the  flask.  In  this  simple  ex- 
periment lies  the  explanation  of  the  recently  attractive 
'  Ghost  phenomena.'  In  this  class  of  illusions  the  back 
part  of  the  stage  is  closed  by  means  of  a  very  large  trans- 
parent piece  of  plate-glass,  somewhat  inclined  forwards, 
through  which  the  audience  perceive  the  players  feebly 
illuminated.  The  e  ghosts  '  with  which  they  appear  to 
communicate  are  the  reflected  images  of  other  persons 
who  are  concealed  from  view,  and  are  in  front  of  and 
below  the  stage ;  these,  however,  in  order  to  give 
sufficiently  bright  reflected  images,  must  be  illuminated 
by  the  electric  or  lime  light. 

18.  In  order  to  direct  the  rays  of  the  sun  into  the 
room  in  a  convenient,  that  is  to  say,  in  a  horizontal 


Fro   19. 


A  HeLiostat. 


direction,  aplane  mirror  is  employed.  To  the  openin  g 
in  the  shutter  is  attached  a  board  (fig.  19)  on  the 
inner  side  of  which  is  a  wide  horizontal  tube,  contain- 
ing the  apparatus  intended  to  be  used  ;  externally 
is  a  mirror,  M,  which  can  be  turned  on  an  axis 
passing  between  two  rods.  The  mirror  can  be  rotated 


REFLEXION   OF  LIGHT. 


33 


Fia.  20. 


on  the  one  hand  around  the  axis  of  the  tube 
by  moving  the  button  A  in  a  semicircular  slit,  and  on 
the  other  hand  it  can  be  inclined  to  the  tube  at  any 
angle  that  may  be  desired  by  turning  the  button  B, 
which  acts  on  the  previously  mentioned  axis  of  the 
mirror  by  means  of  an  endless  screw  and  rack.  It  is 
an  easy  matter  to  direct  the  reflected  rays  of  the  sun 
through  the  tube  by  manipulating  the  buttons  A  and 
J5,  and  to  maintain  them 
in  that  direction  notwith- 
standing the  progressive 
movement  of  the  sun.  This 
apparatus  is  termed  a 
Heliostat. 

The  perpetual  correc- 
tion of  the  position  of  the 
mirror  by  means  of  the 
hand  is,  however,  not  only 
troublesome  but  far  too 
uncertain  and  unsatisfac- 
tory for  all  experiments  re- 
quiring great  steadiness  in 
the  direction  of  the  incident 
rays.  A  Heliostat  has  ac- 
cordingly been  constructed , 
the  mirror  of  which  is  con- 
stantly- presented  to  the  sun  in  the  same  position  by 
means  of  clockwork.  Fig.  20  shows  the  Heliostat  of 
Reusch.  The  axis  of  the  clockwork  011  which  the  lower 
mirror  is  supported  is  placed  parallel  to  the  axis  of  the 
earth,  around  which,  during  the  daily  revolution  of  the 
earth,  the  va/ult  of  heaven,  and  with  it  the  sun,  appears 
to  turn.  The  mirror  is  then  so  placed  that  the  reflected 


Heliostat  of  Reusch. 


34  OPTICS. 

rajs  of  the  sun  course  in  this  axis,  and  are  kept  un- 
altered in  it  by  the  movement  of  the  clockwork.  By 
means  of  a  second  mirror  placed  above,  capable  of  being 
moved  into  any  position  that  maybe  required,  the  beams 
of  light  can  be  made  to  travel  in  the  desired  horizontal 
direction. 

19.  The  principle  of  the  method,  based  on  the  re- 
flexion of  light,  by  which  the  angles  of  the  surfaces 
of  prisms,  crystals,  etc.,  are  measured  may  now  be 

FIG  21. 


Principle  of  the  Reflecting  Goniometer. 

described.  Fig.  21  represents  a  horizontal  circle,  di- 
vided at  its  border  into  360° ;  at  its  middle  is  a  small 
plate,  M,  which  revolves,  and  with  which  an  indicator. 
(Alhidade)  A,  pointing  to  the  divisions,  is  connected. 
A  glass  prism  is  placed  upon  the  plate  M  in  such  a 
position  that  its  angles  and  polished  surfaces  are  vertical. 
A  small  beam  of  the  parallel  rays  of  the  sun,  directed 
into  the  chamber  through  a  vertical  slit  by  means  of  a 
Heliostat,  is  reflected  from  the  anterior  surface  and 
forms  a  bright  vertical  line  upon  a  screen,  S,  placed  at 
the  side.  The  indicator,  A,  and  with  it  the  prism,  is 


REFLEXION   OF   LIGHT.  85 

now  turned  until  a  second  surface  of  the  prism  reflects 
the  rays  in  the  same  direction,  that  is  to  say,  until  the 
bright  line  occupies  the  same  position  on  the  screen. 
The  second  surface  must  now  of  course  occupy  the  same 
position  as  the  first  was  in  previously.     If  the  second 
surface  be  parallel  to  the  first,  it  is  obvious  that  the  in- 
dicator must  revolve  through  180°  to  bring  the  bright 
spot  to  the  same  place,  but  if  the  second  surface  forms 
with  the  second  any  angle  a,  the  object  is  attained  by 
a  revolution  of  180  —  a  degrees.     In  order  therefore  to 
obtain  a  knowledge  of  the   angle  a   between  the  two 
surfaces  of  the  prism,  it  is  only  necessary  to  subtract  the 
angle  of  revolution  of  the  indicator,  which  can  be  read 
off  on  the  divisions  of  the  circumference,  from  180°. 

Instruments  constructed  on  this  principle,  and 
adapted  for  the  exact  measurement  of  the  angles  at 
which  the  surfaces  of  prisms  are  placed  to  one  another, 
are  called  reflecting  goniometers. 

20.  As  the  reflected  rays  proceed  from  •  the  image 
behind  a  mirror  exactly  as  they  would  from  an  object 
placed  in  that  position,  every  reflected  image  must  act 
as  a  material  object  in  regard  to  a  second  mirror,  and  this 
again  is  in  a  position  to  furnish  a  reflected  image.  By 
arranging  two  mirrors  so  that  their  reflecting  sur- 
faces are  turned  towards  each  other,  there  are  pro- 
duced, besides  the  two  reflected  images  of  the  first 
order,  still  others  of  the  second,  third,  and  higher  orders, 
which,  however,  continually  become  fainter  in  conse- 
quence of  the  loss  of  light.  Hence  when  a  lighted 
candle  is  held  between  two  mirrors  placed  opposite  to 
one  another,  we  see  an  indefinite  succession  of  flames 
which  appear  to  be  lost  in  infinite  distance.  The  num- 
ber of  reflections  becomes  limited  as  soon  as  the  two 


\Sy^L^+>^+ 


36 


OPTICS. 


FIG.  22. 


mirrors  form  an  angle  with  each  other.  In  fig.  22 
the  two  mirrors  furnish  the  reflexions  of  the  first 
order,  B  and  B',  of  the  object  situated  between  them. 
Since  the  image  B  behind  the  first  mirror  sends  its  rays 
to  the  second  mirror,  this  gives  an  image  or  reflexion 
of  the  second  order,  (7,  and  similarly,  the  first  mirror 
gives  a  reflexion,  0,  of  the  image  B' .  An  observer 
(0)  placed  between  the  mirrors  sees  the  reflexions, 
in  addition  to  the  object,  regularly  disposed  upon  a 

circle  described  around  the 
point  of  d^cussation  of  the 
two  mirrors,  an  image  ap- 
pearing at  each  angle  space 
which  is  equal  to  the  angle 
of  the  two  mirrors.  The  ob- 
server, 0,  therefore,  sees  the 
object  as  often  as  the  angle 
between  the  two  mirrors  is 
contained  in  360°. 

The  pretty  effects  ob- 
tained in  the  well-known 
plaything  termed  the  ka- 
leidoscope result  from  the 
regular  disposition  of  the 

images  reflected  by  mirrors  placed  at  an  angle.  An 
instrument  of  this  kind  may  be  purchased  for  a  few  pence 
in  every  toyshop.  It  is  composed  of  a  papier-mache  tube 
in  which  are  two  mirrors  inclined  to  one  another  at 
an  angle  ofj30°.  To  the  front  end  is  attached  a  cap, 
capable  of  being  rotated  and  containing  in  its  interior 
two  plates  of  glass,  the  outer  one  of  which  is  ground 
dull.  Between  the  two  plates  are  a  number  of  pieces 
of  differently  coloured  glass,  and  other  small  variegatad 


Angular  mirror. 


REFLEXION  OF  LIGHT.  87 

objects.  If  the  tube  be  placed  in  a  horizontal  position, 
and  the  plate  of  ground  glass  be  illuminated  with  a 
powerful  light,  a  six-rayed  star  will  be  seen  upon  the 
opposite  screen,  decorated  with  the  richest  ornamenta- 
tion.* This  is  the  reflexion  in  the  mirror  of-  the 
fragments  of  glass  which  are  combined  to  form  this 
regular  mosaic.  If  the  cap  be  turned,  the  pieces  of 
glass  constantly  form  new  combinations,  and  thus  an 
inexhaustible  succession  of  the  most  delicate  forms  a,re 
obtained  which  the  liveliest  fancy  could  scarcely  invent. 
What  may  in  this  way  be  represented  for  a  large 
number  of  persons,  as  if  it  were  an  object  on  the  screen, 
can  also  of  course  be  seen  separately  by  every  one  who 
looks  into  the  tube  for  himself. 

21.  Not  only  this  ingenious   plaything,  but  an  in- 


FIG.  23. 


\! 
I) 

Principle  of  the  mirror  sextant. 

strument  of  high  practical  value,  is  founded  on  tl><; 
mutual  action  of  two  mirrors  placed  at  an  angle  to  one 
another.  In  fig.  23,  A  and  B  are  two  small  mirrors, 

*  In  this  experiment  a 'lens  of  short  focus  is  placed  at  the  front  end  of 
the  kaleidoscope. 


33  OPTICS. 

the  reflecting  surfaces  of  which  are  turned  towards 
each  other.  If  two  objects  are  placed  at  L  and  R,  of 
which  the  former  is  visible  to  an  observer  at  0,  above 
the  edge  of  the  mirror  B,  in  the  direction  OB,  the 
mirror  A  may  have  such  a  position  given  to  it  that 
the  light  coining  from  R  reaches  the  eye  after  double 
reflexion  in  the  direction  R  A  B  0,  and  consequently 
two  objects  are  seen  in  the  same  direction,  0  B,  the  one 
direct,  the  other  reflected.  Thus  it  results  from  the  law 
of  reflexion  that  the  angle  a  which  is  included  by  the 
visual  lines  extending  from  the  eye  to  L  and  R,  is  exactly 
twice  as  large  as  the  angle  {3  which  the  two  planes  of  the 
mirrors  form  with  one  another.*  In  order  to  measure 
the  angle  ft  conveniently,  the  mir- 
ror A  is  made  to  rotate  around  the 
axis  of  a  divided  arc,  M  N,  and 
is  connected  with  an  indicator,  A  Z. 
The  mirror  B  is  permanently  fixed 
on  the  plane  of  the  arc  parallel 
to  the  radius  A  M  which  goes  to 
the  zero  of  the  division.  If  any 

Mirror  or  reflecting  sextant.       object,  L,  be  nOW  looked  at    in  the 

direction  0  L  through  a  telescope 

attached  to  the  instrument  (fig.  24)  and  the  indicator, 
and  with  it  the  mirror,  be  rotated  until  the  image  of  R 
is  seen  in  this  direction,  twice  the  angle  read  off  by  the 

*  If  the  perpendiculars  A  E  and  B  D,  which  if  sufficiently  prolonged  cut 
one  another  in  the  point  D  at  an  angle  ft  are  erected  upon  the  mirror  planes, 
it  follows  if  <p  and  fy  indicate  the  angle  of  incidence  of  the  rays  R  A  and  A  B 
on  the  mirrors  A  and  B  from  the  consideration  of  the  triangle  A  B  D 

0=0-^ 

and  from  the  consideration  of  the  triangle  A  0  B 

a=2<p  —  2\J/ 

from  whence  it  immediately  follows  that  o  =  2£. 


REFLEXION   OF  LIGHT.  39 

indicator  immediately  gives  the  angle  which  the  visual 
lines  directed  towards  L  and  R  form  with  each  other. 

This  ingenious  angle  measurer,  conceived  by  New- 
ton and  constructed  by  Hadley,  is  termed  the  reflecting 
sextant.  It  is  superior  to  other  instruments  made  for 
this  purpose  because  it  needs  no  support,  but  during 
the  act  of  measuring  the  angle  can  be  held  freely  in 
the  hand.  Hence  for  nautical  purposes  it  is  the  only 
available  angle-measuring  instrument.  By  means  of 
the  reflecting  sextant  the  seafarer  makes  those  measure- 
ments by  Avhich  he  determines  the  latitude  and  longi- 
tude of  his  ship.  The  two  almost  invisible  mirrors 
enable  him  to  pursue  his  predetermined  course  through 
the  pathless  waste  of  waters. 


40 


OPTICS. 


FIG.  2f>. 


CHAPTER  IV. 

SPHERICAL    MIEEOES. 

22.  A  spherical  shell,  the  inner  surface  of  which  is 
highly  polished,  is  called  a  spherical  concave  mirror. 
It  may  be  regarded  as  a  portion  of  a  hollow  sphere  cut 
off  by  a  plane  M  M',  fig.  25.  A  perpendicular,  c  d,  let 

fall  from  the  centre,  c,  of  the 
sphere  of  which  the  mirror  is  a 
segment  upon  this  plane,  will 
strike  the  middle  point  of  the 
mirror,  and  is  termed  its  prin- 
cipal axis.  The  angle  M  c  M'9 
which  the  lines  Me  and  M' c, 
drawn  from  two  diametrically 
opposite,  points  of  the  periphery 

of  the  mirror  to  the  centre  of  the  sphere  form  with  one 
another,  is  called  the  aperture  of  the  mirror.  In 
practice,  only  mirrors  of  small  aperture  are  in  use,  in 
which  this  angle  amounts  at  most  to  six  or  eight  degrees, 
and  the  remarks  here  made  will  only  have  reference  to 
these. 

If  a  beam  of  parallel  solar  rays,  thrown  horizontally 
into  the  chamber  by  means  of  the  Heliostat,  be  allowed 
to  fall  upon  a  concave  mirror  with  small  aperture 
parallel  to  its  axis  (fig.  26),  it  will  be  seen — for  the 
path  of  the  rays  can  be  distinctly  followed  by  the  illu- 


Concave  mirror. 


SPHERICAL  MIRRORS.  41 

mination  of  the  particles  of  dust  always  present  in  the 
air  of  a  room  — that  it  is  reflected  in  the  form  of  a  cone 
of  light,  the  apex  of  which,  F,  lies  in  front  of  the  mirror 
in  this  axis.     This  point,  _F,  through  which  all  the  rays 
falling   on    the   mirror  parallel 
to  its  axis  pass  after  reflexion, 
is  called  the  focus.     It  becomes 
brilliantly  luminous  if  I  throw 
some  dust   into  the   air  in  its 
vicinity.     It  appears  as  a  white 
spot  of  dazzling  brilliancy  when 

a  white  sheet  of  paper  is  held  in  it,  and  the  wreaths 
of  smoke  that  are  now  rising  from  it  show  you  that 
the  paper  has  caught  fire  in  the  intense  heat  of  the  rays 
collected  at  this  point,  and  that  it  has  consequently 
been  appropriately  named  the  focus  or  burning-point 
(Brennpunkt).  The  space  intervening  between  the 
focus  and  the  mirror — the  focal  distance — can  easily 
be  measured,  and  is  found  to  be  equal  to  half  the  radius 
of  curvature  of  the  mirror,  or  in  other  words,  the  focus 
lies  midway  between  the  mirror  and  the  centre  of  the 
circle  of  which  it  is  a  segment. 

23.  The  reflexion  of  a  ray  of  light  from  a  curved 
surface  follows  the  same  law  as  from  a  plane  surface ; 
the  portion  of  the  curve  which  immediately  surrounds 
the  minute  point  of  incidence  on  that  each  ray  of  light 
impinges  can  alone  be  considered  to  act  as  a  reflector. 
The  smaller  we  admit  the  superficial  area  of  this  part  to 
be — and  we  may  conceive  it  to  be  as  small  as  we  please 
— so  much  the  more  accurately  can  we  regard  it  as  a 
small  plane  mirror,  and  the  perpendicular  erected  upon 
this  is  then  the  axis  of  incidence  in  regard  to  which 
the  incident  and  the  reflected  ray  behave  as  has  been 


42  OPTICS. 

stated.  Concave  differ  only  from  plane  mirrors  in  the 
circumstance  that  each  point  has  its  own  axis  of 
incidence. 

Since  every  radius  of  a  spherical  surface  is  perpen- 
dicular to  the  surface  where  it  meets  it,  we  obtain 
the  axis  of  incidence  of  a  spherical  concave  mirror  by 
simply  drawing  the  corresponding  radius  to  the  point 
of  incidence. 

In  a  concave  mirror  of  small  aperture  the  axes  of 
incidence,  that  is  to  say,  the  radii,  are  more  and  more 
strongly  inclined  to  the  principal  axis  in  proportion  as 
the  corresponding  points  of  the  mirror  are  more  distant 

L  *J        L  */ 

from  it.  Hence  every  ray  of  light  running  parallel  to  the 
axis  must  be  inclined  from  its  original  direction  more 
and  more  strongly  towards  the  axis  in  proportion  as  it 
strikes  the  mirror  at  a  point  more  distant  from  the 
axis.  This,  which  is  clearly  exhibited  in  fig.  26,  ex- 
plains why  all  rays  falling  on  the  mirror  parallel  to  its 
axis  must  pass  through  a  single  point  after  reflexion. 

24.  From  the  above-mentioned  direction  of  the  axes 
of  incidence,  it  follows  further  that  all  rays  proceeding 
from  a  point  pass  through  a  single  point  after  reflexion, 
because  they  undergo  a  change  in  their  direction  greater 
in  proportion  as  the  point  of  the  mirror  struck  is  dis- 
tant from  the  principal  axis. 

FIG.  27. 


Conjugate  foci. 

In  the  concave  mirror,  fig.  27,  which  is  supported 
on  a  stand,  two  indicators  (omitted  in  the  figure)  point 
to  the  principal  focus  F,  and  the  centre  of  the  sphere  o. 


SPHERICAL  MIRRORS.  43 

At  the  point  A  in  the  axis,  the  light  of  an  electric  lamp 
is  placed,  which,  to  protect  the  eye  from  its  glare,  is 
enclosed  in  a  box  having  only  a  round  opening  on  the 
8ide  turned  towards  the  mirror.  A  diverging  cone  of 
rays  proceeding  from  the  luminous  point  A  passes  to  the 
mirror  and  is  reflected  forwards  from  it  as  a  converging 
cone,  the  apex  of  which  lies  at  a  in  the  axis  of  the  mirror, 
between  the  focus  and  the  centre  of  the  sphere.  This 
point  of  union  of  the  reflected  rays  is  called  the  image 
of  the  point  A.  If  the  luminous  point  A  be  approxi- 
mated to  the  mirror,  the  point  at  which  the  rays  unite, 
a,  retreats  from  the  mirror  towards  the  centre  C;  if  the 
luminous  point  be  placed  at  C,  every  ray  it  emits  strikes 
perpendicularly  upon  the  surface  of  the  mirror,  and 
is  therefore  reflected  upon  itseli ;  and  thus,  when  it  is 
situated  in  the  centre  of  the  circle  of  curvature,  the 
light  and  the  reflected  image  of  the  light  are  coincident. 
If,  on  the  other  hand,  the  light  be  removed  from  A  to  a 
greater  distance  from  the  mirror,  its  image  continues 
to  approach  the  focal  point,  and  would  ultimately 
coincide  with  it  were  it  possible  to  remove  the  light  to 
an  infinite  distance.  The  removal  of  the  luminous  point 
to  infinite  distance,  which  it  is  of  course  impossible  to 
accomplish,  has  been  effected,  however,  in  the  foregoing 
experiment  (fig.  26),  for  rays  which  run  parallel  with 
the  axis  may  be  regarded  as  coming  from  a  point  on 
the  axis  at  an  infinite  distance,  and  they  are,  as  has 
been  seen,  united  in  the  focus. 

It  is  further  intelligible  that  rays  of  light  which, 
proceeding  from  the  point  a,  strike  upon  the  mirror,  are 
reflected  to  the  point  A,  pursuing  the  samo  course  but 
in  the  opposite  direction ;  in  other  words,  if  a  luminous 
point  a  lies  between  the  focus  and  the  centre  of  the 


44  OPTICS. 

sphere,  its  image  is  situated  at  A  on  the  other  side  of 
the  centre.  The  two  points,  A  and  a,  are  thus  so  asso- 
ciated that  each  constitutes  the  image  of  the  other,  and  they 
are  hence  called  corresponding  or  conjugate  points.  To 
the  focus  itself  consequently,  an  infinitely  remote  point  is 
conjugate ;  that  is  to  say,  rays  which  proceed  from  the 
focus  and  strike  the  mirror  are  reflected  parallel  to  the 
principal  axis  to  an  infinitely  remote  distance.  If  we 
place  the  luminous  point  (A,  fig.  28)  nearer  than  the  focus 
to  the  mirror,  this  is  no  longer  capable  of  collecting  the 


Fia.  28. 


Conjugate  points. 

too  strongly  diverging  rays,  and  the  reflected  rays 
diverge  as  if  they  proceeded  from  a  point  a,  situated 
behind  the  mirror;  and  so  conversely,  since  rays  which 
converge  towards  a  point  a  behind  the  mirror,  are 
united  in  the  point  A  in  front  of  the  mirror,  the  two 
points  A  and  a  may  be  regarded  as  conjugate  points. 

25.  Hitherto  the  case  of  luminous  points  lying  in 
the  principal  axis  of  the  mirror  has  alone  been  con- 
sidered. The  electric  lamp  must  now  be  placed  in  such 
a  position  that  its  luminous  point  lies  above  the  axis  (at 
A,  fig.  29).  It  will  then  be  seen  that  the  reflected  rays 
unite  in  a  single  point  B,  but  this  lies  below  the  axis  on 
the  straight  line  which  may  be  conceived  to  be  drawn 
from  the  luminous  point  A,  through  the  centre  of  the 


SPHERICAL  MIRRORS,  45 

sphere  0,  to  the  mirror.  Amongst  all  the  rays  which 
proceed  from  A  and  strike  upon  the  mirror,  that  passing 
through  C  is  the  only  one  that  falls  perpendicularly  upon 
the  mirror,  and  is  therefore  reflected  upon  itself.  The 
straight  line,  A  0,  holds  therefore  the  same  relation  to 


FIG.  29. 


Conjugate  points  on  a  secondary  axis. 

the  principal  laterally-situated  point  A  as  the  axis,  C  F, 
has  to  the  previously-considered  position  of  the  lumi- 
nous point;  it  is  termed  therefore  the  secondary  axis  cor- 
responding to  the  point  A.  For  every  secondary  axis, 
the  number  of  which  is  of  course  infinite,  the  same 
holds  that  has  already  been  stated  in  reference  to  the 
chief  axis,  each,  for  example,  has  its  own  focus  in 
which  the  rays  parallel  with  it  meet. 

The  peculiarities  of  concave  mirrors,  as  far  as  they 
have  hitherto  been  considered,  may  be  summed  up  in 
the  following  propositions  :  All  rays  that,  before  they 
fall  upon  the  mirror,  proceed  from  a  point  or  travel 
towards  a  point,  pass,  after  reflexion,  through  a  single 
point  (either  actually  or  when  prolonged)  which  iies  on  the 
axis  corresponding  to  the  first  point.  These  two  points 
are  so  conjugated  that  the  one  is  the  image  of  the  other. 

26.  Inasmuch  as  to  every  point  of  a  luminous  or 
illuminated  object  situated  in  front  of  a  concave  mirror 
there  is  a  corresponding  image-point  situated  on  the 
axis  belonging  to  it,  it  follows  that  from  the  collection 
of  all  the  image-points  an  image  of  the  object  results. 


46 


OPTICS. 


Now  let  a  lighted  candle  be  placed  betiveen  the  focus 
and  the  centre  of  curvature  of  the  mirror*  (fig.  80).  The 
place  of  the  image  can  easily  be  found  by  moving  to  and 
fro  a  paper  screen,  situated  on  the  other  side  of  the 
centre  of  curvature,  and  protected  from  the  direct  rajs 


FIG. 


Real  image. 

of  the  flame  by  a  small  blackened  metal  disk.  An  in- 
verted and  enlarged  image  of  the  flame  is  then  obtained 
upon  the  screen,  as  is  shown  in  fig.  31,  in  which  the 
course  of  the  rays  of  light  for  the  point  B  of  the  object 
A  B  is  indicated,  showing  how  the  inverted  enlarged 
image  a  b  is  formed. 

FIG.  31. 


Production  of  real  images. 

If,  as  in  this  figure,  all  the  points  of  the  object  are 
found  in  a  single  plane  (A  B)  perpendicular  to  the  axis, 
the  points  of  the  image  (always  presupposing  the 

*  In  the  figure  the  focus  is  found  over  the  number  132,  the  centre  of 
the  curvature  orer  120. 


SPHERICAL  MIRRORS.  47 

aperture  of  the  mirror  to  be  small)  lie  also  in  a  plane 
perpendicular  to  the  axis.  It  is  obvious  also,  from  the 
drawing,  that  image  and  object  are  similar  to  each 
other,  and  their  relative  sizes  are  as  their  distances  from 
the  mirror. 

Supposing  a  &  to  be  an  object  situated  at  more  than 
twice  the  focal  distance  from  the  mirror,  an  inverted  and 
diminished  image  at  A  B  will  correspond  to  it,  lying  be- 
tween the  focal  point  and  the  centre  of  curvature.  The 
further  the  object  is  from  the  mirror  the  closer  is  the 
image  to  the  focus,  and  the  image  of  an  indefinitely 
remote  object,  of  a  star  for  example,  is  situated  in  the 
focal  point  itself. 

These  images  are,  however,  essentially  different  from 
those  of  plane  mirrors.  They  are  produced  by  the 
actual  union  in  front  of  the  mirror  of  the  rays  proceeding 
from  every  point  of  the  object.  They  may  be  received 
upon  a  screen  and  thus  be  made  visible  on  all  sides  by 
diffuse  reflexion,  as  if  the  image  were  itself  a  luminous 
object.  Such  images  are  consequently  called  actual  or 
real  images.  The  images  of  plane  mirrors,  on  the  other 
hand,  are  produced  by  rays  which  appear  to  proceed 
from  points  lying  behind  the  surface  of  the  mirror,  and 
are  only  seen  when  these  rays  pass  directly  into  the 
eye*  These  are  consequently  termed  apparent  or  virtual 
images. 

Real  images  may  be  directly  seen  without  any 
recipient  screen  if  the  observer  be  in  the  path  of  the 
rays  which  are  again  diverging  after  the  union  of  the 
points  of  the  image.  The  image  appears  in  these  cases 
to  float  in  the  air  in  front  of  the  mirror.  Aerial  images 
of  this  kind  produce  the  most  surprising  phenomena. 
For  example,  a  beautiful  bunch  of  flowers  may  be  made 


48 


OPTICS. 


to  float  over  a  table ;  it  is  the  real  image  of  a  group  of 
artificial  flowers  placed  in  an  inverted  position  before  a 
concave  mirror  and  strongly  illuminated,  but  concealed 
from  the  eye.  If  now  a  vase  be  placed  upon  the  table 
in  which  the  bunch  appears  to  be  inserted,  it  can  easily 
be  shown  by  moving  the  head  to  and  fro  that  the  bunch 
remains  in  the  vase,  proving  therefore  that  the  image 
is  in  front  of  the  mirror  directly  above  the  vase. 

27.  Concave  mirrors  only  furnish  real  images  of 
objects  which  are  more  distant  than  the  principal  focus 
from  the  mirror.  They  can  only  give  an  apparent 
or  virtual  image  of  any  object  which  is  nearer  than  the 

FIG.  32. 


Production  of  a  virtual  image. 

principal  focus,  because  the  ra}^s  of  light  coming  from 
each  point  are  reflected  in  a  diverging  manner  (see 
fig.  28),  and  this  image  appears  to  an  eye  looking  into 
the  mirror  as  erect,  behind  the  surface  of  the  mirror, 
and  larger  than  the  object.  Fig.  32  shows  the  course 
of  the  rays  in  the  opposite  case.  In  consequence  of 
this  enlarging  action,  concave  mirrors  are  termed  mag- 
nifying mirrors,  and  are  often  employed  in  the  toilet  as 
shaving-glasses,  etc.  An  object  placed  at  the  principal 
focus  of  the  mirror  gives  neither  a  real  nor  a  virtual 


SPHERICAL  MIRRORS.  49 

image,  for  the  rays  proceeding  from  each  part  of  it  are 
reflected  parallel  to  their  own  secondary  axes.  If  a 
source  of  light  be  brought  into  the  principal  focus  of 
a  concave  mirror,  the  reflected  rays  proceed  to  great 
distances  unimpaired  in  brilliancy,  because  they  run 
together  as  parallel  rays.  Hence  the  application  of 
concave  mirrors  as  reflectors  (Reverberen,  see  fig.  4,  0} 
for  the  electric  illumination  of  workshops  during  night 
work,  and  for  lighthouses. 

28.  In  spherical  convex  mirrors  the  reflexion  takes 
place  on  the  outside  of  the  curved  surface  of  a  section 
of  a  sphere.  If  the  aperture  of  the  mirror  be  small,  the 
rays  proceeding  from,  or  passing  to,  any  point  diverge 
more  strongly  in  exact  proportion  as  they  fall  on  the 
mirror  more  remotely  from  the  axis,  and  therefore  also, 
after  reflexion,  pass  through  a  single  (real  or  virtual) 
image  point. 

Rays  which  fall  parallel  to  a  (principal  or  secondary) 
axis  on  a  convex  mirror  (fig.  33)  diverge  after  reflexion 
as  if  they  proceeded  from 
a  point  F,  which    lies  on 
the    axis    about   half   the 
length   of    the    radius    of 
curvature  behind  the  sur- 
face of  the  mirror.     This 
may    be    termed  the  vir- 
tual principal  foCUS.      Con-  Virtual  principal  focus  of  a  convex 
_  mirror. 

versely,    a    cone    of  rays 

converging  to  this  point  are  reflected  as  a  parallel  beam. 
Rays  which  converge  still  more  strongly,  that  is  to  say, 
to  a  point  nearer  to  the  back  of  the  mirror,  remain  con- 
vergent after  reflexion,  and  unite  in  a  point  in  front  of 
the  mirror.  Thus,  for  example,  in  fig.  34  the  cone  of  rays 


50 


OPTICS. 


FIG.  34 


passing  to  the  point  b  behind  the  mirror,  are  reflected 
towards  the  point  B  in  front  of  the  mirror.  If  the  rays 

proceed  from  a  point  lying 
in  front  of  the  mirror,  they 
strike  it  divergingly,  and 
are  always  reflected  still 
more  divergingly.  Of  any 
object,  whatever  may  be  its 
position  in  front  of  the 
mirror,  only  a  virtual  erect 

image  can  therefore  be  obtained,  and  this  is  perceived 
behind  the  surface  of  the  mirror  and  somewhat  nearer 
to  it  than  the  virtual  principal  focus  (fig.  34).  Since 
the  image  is  always  smaller  than  the  object,  a  convex 
mirror  is  termed  a  diminishing  mirror,  and,  on  account 
of  its  producing  pretty  images,  is  used  as  a  table  toilet 
mirror. 


Production  of  a  virtual  image  behind  a 
convex  mirror. 


FIG.  35. 


APPENDIX  TO   CHAPTER  IV. 

IT  is  not  difficult  to  deduce  the  propositions  respecting  the 
action  of  spherical  mirrors  of  small  aperture  from  simple  geo- 
metrical considerations  connected  with  the  law  of  reflexion,  and 

thus  to  give  them  a  theoretical 
basis.      Before  entering   upon 
these   considerations,  this    op- 
portunity may  be  taken  of  de- 
n   scribing  the  best  method  of  ex- 
pressing the  size  of  any  angle. 
Mode  of  expressing  the  size  of  any  angle..  {     >  & 

The  measure  of  an  angle  is  the 

length  a  (fig.  35)  of  the  arc  of  a  circle  included  between  the  straight 
lines  containing  the  angle,  drawn  with  a  radius  of  any  length  which 
is  taken  as  unity,  and  having  its  centre  at  the  apex  of  the  angle. 
Upon  a  second  circle  described  with  a  radius  C  A  =  p,  the  apex 


SPHERICAL  MIRRORS.  51 

of  the  angle  being  again  the  centre,  the  same  angle  corresponds  to 
the  arc  A  B  =  b,  which  holds  the  same  relation  to  the  arc  a  as 
does  the  radius  p  to  the  radius  1.  From  the  ratio 

a  :  b  =  1  :  p, 

however,  it  follows  that  a  ==  - ;    that  is  to  say,  the  size  of  any 

P 

angle  A  C  B,  or  the  length  of  arc  corresponding  to  it  in  a 
circle  having  a  radius  of  1,  is  always  ibund  by  describing  around 
the  apex  of  the  angle  a  given  circle,  and  dividing  the  length  of 
arc  b  between  the  limbs  by  the  radius  p. 

If  irom  the  point  B,  where  one  of  the  limbs  cuts  the  circle, 
a  perpendicular  k  be  let  fall  upon  the   second  leg,   this,  if  the 
angle  at  C  be  very  small,   is  nearly 
equal  to  the  arc  6,  and  can  be  used  in-  FlG-  8G- 

stead  of  it  without  appreciable  error. 

It  may  be  admitted,  that  is,  a  =  ' 

P 
as  the  measure  of  the  angle  A  C  B. 

-.T          -.  i   /  r>        o/»\    i    *~  *•      Determination  of  the  position  of  the 

Now  let  a  b  (fig.   36)  be  a   ray  of  rrincipai  focal  point, 

light  forming  with   the  radius  C  b 

(the  axis  of  incidence),  the  angle  z,  the  reflected  ray  bg  makes 
with  the  axis  of  incidence  the  corresponding  and  equal  angle  r. 
The  angle  x,  which  the  radius  C  b  and  axis  include,  is  obviously 
equal  to  the  angle  z,  and  consequently  also  to  the  angle  r.  More- 
over, the  angle  b  Fd  which  the  reflected  ray  forms  with  the  axis 
is  equal  to  the  angle  a  b  F,  and  thus  it  is  equal  to  i  +  r,  or  what 
is  the  same  thing, 

b  Fd  =  2x. 

If  a  perpendicular  k  be  now  conceived  to  fall  from  b  upon  the 
axis  of  the  mirror,  and  if  the  radius  of  the  mirror  be  indicated 
by  the  sign  p,  the  angle  x  may  be  expressed  as  follows. 

k 
x  —  — 

P 
and  consequently 

bFd  =  2-; 
P 


52  OPTICS. 

and  it  is  now  clear  that  the  angle  bFd,  that  is  to  say,  the  diver- 
gence of  the  reflected  ray  from  its  original  direction  is  propor- 
tional to  the  distance  k  of  the  point  of  incidence  from  the  axis 
of  the  mirror. 

The  angle  bFdmay,  however,  be  expressed  in  another  way  ; 
for  example,  it  may  be  said 


or  again,  because  on  account  of  the  small  ness  of  the  angle  bFd 
the  line  b  F  is  scarcely  different  from  the  focal  distance  d  F, 
which  we  indicate  by  /, 


This  expression,  compared  with  the  above,  leads  to  the  equation 
k_        k 

7     "7' 

which  enables  the  position  of  the  point  F,  where  the  reflected  ray 
cuts  the  axis,  to  be  determined.  But  since  the  magnitude  &, 
because  it  appears  as  a  factor  on  both  sides  of  the  equation,  may 
be  eliminated,  it  is  obvious  that  the  position  of  the  point  of  inci- 
dence /3  has  no  influence  upon  the  determination  of  the  point  F  ; 

FIG.  37. 


Determination  of  the  position  of  conjugate  points. 

that  is  to  say,  all  rays  coursing  parallel  to  the  axis  pass  after 
reflexion  through  one  and  the  same  point  F,  situated  upon  the 
axis,  the  distance  /  of  which  from  the  mirror  is  determined  by 
the  equation, 


SPHERICAL  MIRRORS.  53 

Tlte  focal  distance  is  consequently  equal  to  half  the  radius. 

If  we  now  consider  any  ray  A  b,  proceeding  from  the  point  A, 
making  (fig.  37)  the  angle  «  with  the  axis,  we  shall  find  that  it  is 
BO  reflected  in  the  point  b  that  the  angle  of  incidence  and  the 
angle  of  reflexion  are  both  =  3,  and  the  reflected  ray  cuts  the 
axis  at  the  point  B  at  an  angle  ft.  If  now  the  angle  which  the 
axis  of  incidence  drawn  towards  b  makes  with  the  axis  be  in- 
dicated by  y,  we  obtain,  because  ft  is  the  external  angle  of  the 
triangle  BCI>  and  y  is  the  external  angle  of  the  triangle  CA  b, 
the  two  equations, 

ft  =  7  +  3 
a  =  y  -  I, 

which  added  together  make 

«  +  b  =  2y; 

that  is  to  say,  for  every  point  of  the  mirror  the  sum  of  the  angles 
which  the  incident  and  the  reflected  ray  make  with  the  axis  is 
inalterable,  and  is  indeed  equal  to  the  deflection  which  the  ray 
passing  to  the  focal  point  experiences  at  the  point. 

If  now  the  focal  length  of  the  mirror  be  indicated  by  /,  and 
its  radius  consequently  by  2/,  and  further,  the  distance  of  the 
luminous  point  d  A  (=  b  A)  by  a,  the  distance  d  B  (=  b  B)  of 
the  image-point  by  b,  arid  the  perpendicular  let  fall  from  the 
point  of  incidence  b  upon  the  axis,  by  &,  we  obtain  from  the 
above-mentioned  method  of  measuring  the  angles, 

/•       ,         k  k 

„  =          p  —          y  = 

a  b  2/ 

and  consequently  if  these  are  arranged  in  rhe  equation  a  +  ft  =  2y 
1          *         A- 

~L     +       I '    —    f  '     °r' 

since  the  common  factor  k  may  be  eliminated, 

a  +  ~b   =  =  /' 

This  very  circumstance,  that  the  magnitude  k,  which  alone 
reft-rs  to  the  position,  whatever  that  may  be,  of  the  point  of 


54  OPTICS. 

incidence,  is  removable  from  the  equation,  supplies  the  proof  that 
all  rays  proceeding  from  the  point  A,  wherever  they  may  strike 
the  mirror,  are  united  in  the  selfsame  point  B. 

From  the  form  of  this  equation,  which  expresses  in  the 
simplest  manner  the  opposite  relation  of  two  conjugated  points,  it 
is  further  evident  that  the  light-point  arid  the  image-point  are 
mutually  interchangeable. 

The  deviation  which  the  ray  incident  in  b  experiences  is  2c. 
But  from  the  above  equation,  it  results  that 


^-*-*(LJ 

\b       a 


The  accuracy  of  the  statement  above  made,  that  the  deflections 
which  the  rays  proceeding  Jrom  any  point  experience  are  propor- 
tional to  the  distances  of  the  points  of  incidence  from  the  axis  of 
the  mirror,  is  thus  rendered  evident. 

in  order  to  determine  the  position  and  size  of  the  image  by 
construction  it  is  not  necessary  to  draw  a  great  number  of  rays, 
as  in  figs.  31,  32,  and  34;  but  only  two  rays  for  each  point  of 

FIG.  '8. 


Construction  showing  the  for  n  atton  of  the  image. 

the  image,  because  the  others  necessnrily  meet  at  point  where 
these  decussate.  The  two  rays  selected  should  be  such  as  to 
make  the  construction  as  neat  and  convenient  as  possible.  In 
fig.  38  the  object  whose  image  is  to  be  determined  is  a  straight 
line  A  a,  perpendicular  to  the  principal  axis.  Let  the  secondary 
axis  A  C  be  drawn  to  the  point  A  ;  the  ray  coursing  in  this 
axis  is  of  course  reflected  upon  itself.  Now  let  the  ray  parallel 
to  the  principal  axis  be  drawn ;  this  passes  after  reflexion  through 
the  principal  focus,  and  the  image  of  the  point  A  required  lies  at 
the  point  I?,  where  it  cuts  the  secondary  axis  A  (7,  and  if  B  b  be 


SPHERICAL  MIRROKS.  ftfi 

let  fall  perpendicularly  to  the  chief  axis  we  obtain  in  B  b  the 
image  of  the  object  A  a. 

The  course  of  all  other  rays  proceeding  from  A  may  now  be 
followed  with  facility.  Thus,  for  example,  the  ray  A  0,  whicl 
strikes  the  centre  of  (he  mirror  o,  is  reflected  in  the  direction  o  B 
And  as  at  the  point  o  the  principal  axis  is  the  axis  of  incidence, 
the  angle  Aoaia  equal  to  the  angle  B  o  b.  If  the  magnitude 
of  the  object  A  a  be  indicated  by  the  sign  />,  the  magnitude  ol 
the  image  Bb  by  the  sign  </,  and  the  distances  of  the  object  and 
of  the  image  from  the  mirror  as  before  by  the  s?igns  a  and  b,  it  is 
clear  that 

p  :  q  =  a  :  b; 

that  is  to  say,  the  size  of  the  object  stands  in  the  same  relation  to 
t lie  size  of  the  image  as  the  distance  of  the  former  from  the  mirror 
is  to  the  distance  of  the  latter  from  the  mirror,  a  proposition  that 
holds  equally  for  the  virtual  as  for  the  real  image.  The  equa- 
tions that  have  been  deduced  in  the  case  of  concave  mirrors  hold 
also  for  convex  ones,  if  the  virtual  focal  distance  be  regarded  art 
negative,  that  is  to  say,  as  —/instead  of/. 


56 


OPTICS. 


CHAPTER    V. 

REFRACTION. 

29.  THE  adjoining  figure  (fig.  39)  represents  a  cubic 
vessel  the  sides  of  which  are  made  of  glass.  A 
beam  of  parallel  rays  of  light  from  the  sun  directed 
horizontally  into  the  room  by  means  of  the  Heliostat 


Refractor. 


is  thrown  obliquely  upon  the  surface  of  the  water  by 
a  small  mirror.  A  part  of  the  rays  is,  in  accord- 
ance with  known  laws,  reflected  at  the  surface  of  the 
water,  whilst  another  portion  penetrates  it  ;  this  last, 
however,  does  not  pursue  a  course  directly  continuous 
with  the  incident  rays,  but  follows  a  steeper,  though  still 
always  straight  direction.*  'j 


*  The  course  of  the  incident  and  reflected  rays  cf  light  in  the  air  is 
readily  recognised  by  the  illumination  of  floating  particles  of  dust,  and  in 


REFKACTION. 


57 


It  thus  appears  that  the  rays  of  light,  as  they  pass 
from  the  air  into  the  water,  are  bent  or  refracted,  and 
the  term  refraction  is  accordingly  employed  to  indicate 
the  phenomenon  that  is  here  observed. 

The  deviation  of  the  refracted  beam  of  light  from 
its  original  direction  is  smaller  in  proportion  as  by 
turning  the  mirror  A  the  rays  are  made  to  fall  more 
vertically  upon  the  surface  of  the  water  until,  when  they 
come  to  fall  quite  perpendicularly,  they  undergo  no 
change  of  direction  at  all,  the  rays  that  enter  the  water 
pursuing  the  same  direction  they  previously  had  in  the 
air. 

In  order  to  follow  the  exact  course  of  a  ray  of 
light  as  it  passes  from  the  air  into  water,  or  gener- 

FiG.  40. 


-u,  ^  JL 


Angles  of  incidence  and  of  refraction. 


ally  from  any  one  transparent  medium  into  another,  let 
any  point,  n  (fig.  40)  be  taken,  where  the  incident  ray 

order  to  make  it  apparent  in  the  water  a  small  quantity  of  a  fluorescent 
substance,  sesculin,  may  be  added. 


58  OPTICS. 

strikes  the  surface,  and  upon  this  erect  the  perpendicu- 
lar or  axis  of  incidence,  n  m,  and  let  this  be  prolonged 
into  the  second  medium  (nmf).  We  now  observe,  in 
the  first  place,  that  the  plane  which  contains  the  incident 
ray  and  the  axis  of  incidence.,  always  also  contains  the 
refracted  ray.  It  is  hence  termed  the  plane  of  refrac- 
tion. The  direction  of  the  ray  is  determined  by  the 
angle  which  the  ray  makes  with  the  axis  of  incidence, 
namely  by  the  angle  of  incidence  i  and  the  angle  of 
refraction  r.  The  angle  d  between  the  refracted  ray 
n  q  and  the  continuation  n  p'  of  the  incident  ray, 
gives  the  amount  of  deflection  which  the  ray  under- 
g:es  in  its  refraction. 

30.  From  the  experiment  given  above  it  may  be  in- 
ferred that  in  the  passage  of  a  beam  of  light  from  air 
into  water  the  angle  of  refraction  is  always  less  than 
the  angle  of  incidence,  and  that  if  the  angle  of  inci- 
dence increases,  the  angle  of  refraction  and  the  deflec- 
tion of  the  ray  also  increase.  In  order  to  obtain  a 
more  thorough  insight  into  the  whole  process  the  rela- 
tion that  exists  between  the  size  of  the  angle  of  inci- 
dence and  that  of  the  angle  of 
.  41.  refraction  must  be  investigated, 

and  to  accomplish  this  it  is 
necessary  to  measure  the  two 
angles  in  question. 

Fig.  41  shows  a  convenient 
apparatus  for  this  purpose.  The 
flat  side  of  a  semicircular  vessel 

Apparatus  for  demonstrating  the  ..  _          ,  ,          _ 

law  of  refraction.  is    made     of     glass,     rendered 

opaque    except    at   the    centre, 

where  there  is  a  vertical  transparent  slit.  The  internal 
surface  of  the  semicircular  wall  is  divided  into  90° 


REFRACTION.  59 

towards  each  side,  commencing  from  a  point  exactly 
opposite  the  slit.  The  vessel  is  half  filled  with  water  : 
the  upper  half  of  a  horizontal  beam  of  light,  entering 
the  vessel  through  the  slit,  pursues  its  original  course 
above  the  level  of  the  water,  the  lower  half,  on  the  other 
hand,  experiences  refraction  in  the  water.  The  glass 
plate  a  b  *  represents  the  limiting  refracting  plane  be- 
tween the  external  air  and  the  water,  and  the  horizon- 
tal line  drawn  from  the  zero  point  of  the  scale  to  the  slit, 
the  axis  of  incidence.  By  making  the  vessel  assume 
different  positions  in  relation  to  ihe  incident  rays,  the 
angle  of  incidence  can  be  varied  to  any  extent,  and  the 
angle  of  incidence  of  the  ray  passing  over  the  surface  of 
the  water,  and  the  angle  of  refraction  of  the  ray  passing 
through  the  water,  can  be  read  off  on  the  scale. 

We  find,  for  example,  with  an  angle  of  incidence  of 

16°  the  angle  of  refraction  is  11'^-° 

30°  „  22° 

45°  „  82° 

60°  „  40  i° 


31.  In  accordance  with  this  little  table,  the  angle  of 
incidence  i  being  equal  to  60°,  the  angle  of  refraction 
r  =  40^°.  If  we  now  describe,  in  the  plane  of  refraction, 
a  circle  with  the  point  of  incidence  n  as  centre,  arid  let 
fall  from  the  points  a  and  b,  at  which  the  incident  and 
refracted  rays  cut  the  circle,  the  perpendiculars  ad  and 
bf  upon  the  axis  of  incidence,  it  follows  that  bf  is 
exactly  J  of  at?,  or  ad  ±  of  bf.  On  repeating  this 
construction  for  all  the  pairs  of  angles  in  the  above 

*  It  will  presently  be  shown  that  this  exercises  no  influence  on  the 
direction  of  the  ra.vs  traversing  it. 


60  OPTICS. 

table,  we  constantly  find  that  the  perpendicular  corre- 
sponding to  the  angle  of  incidence  is  exactly  •£  as  large 
as  that  belonging  to  the  angle  of  refraction.     The  number 
-f  or  1±,  which  may  be  regarded  as 
the  measure  for  the  amount  of  re- 
fraction light  undergoes  in  passing 
from  air  into  water,  is  termed  the 
index  of  refraction,  or  the  coefficient 
of  refraction  of  water.     In  passing 
^~-  from  air  into  glass  the  rays  of  light 

are  more   strongly  refracted,  and 

^--^--    ~- ">-•  •-— -  ---:----=-  ^  6     J 

the  relation  of  these  two  perpen- 

Law  of  refraction.  "        * 

diculars  is  expressed  by  the  frac- 
tion |  or  1-5.  In  this  way  every  transparent  substance* 
has  its  own  refractive  power.  The  following  table 
shows,  in  regard  to  a  few  of  these,  the  ratio  of  refrac- 
tion for  light  in  passing  into  them  from  air : — 

Water       .         .         .         .  1-333 

Alcohol      .         »         .        V  1-365 

Canada  balsam  .         .         .  1*530 

Carbonic  disulphide  .      '   .  1*631 

Crown  glass       .         .         .  1*530 

Mint  glass  (Fraunhofer)    .  1-635 

Flint  glass  (Merz)      '&      .  1-732 

Diamond  .         .        "V~  .,_.  2*487 

In  geometry  the  perpendiculars  a  d  and  If  (fig.  42), 
when  the  radius  of  the  circle  =  1,  are  termed  the 
f  sines'  of  the  angles  i  and  r,  and  the  law  of  refraction 
can  be  expressed  in  the  following  terms  : 

The  sines  of  the  angle  of  incidence  and  refraction 
stand  in  an  invariable  relation  to  each  other. 

If  the  ratio  of  refraction  be  designated  by  n,  this 


EEFRACTION. 


61 


law  can  be  rendered  easily  intelligible  by  the  following 
simple  expression — 

sin  i  =  n  sin  r, 

that  is  to  say,  the  sine  of  the  angle  of  incidence  is 
equal  to  n,  multiplied  into  the  sine  of  refraction. 

If  the  angle  of  incidence  be  very  small,  by  so  much 
the  smaller  is  the  angle  of  refraction,  for  then  the  arcs 
which  correspond  to  these  angles  do  not  materially 
differ  from  the  sines,  and  may  therefore  be  taken 
instead  of  them,  and  then  the  law  of  refraction  assumes 
a  still  simpler  form,  namely— 

i  •=.  n  r, 

that  is  to  say,  with  nearly  perpendicular  incidence  of 
the  ray,  the  angle  of  incidence  is  n  times  as  great  as 
the  corresponding  angle  of  refraction. 

32.  Hitherto  the  passage  of  light  from  air  into  a 
fluid  or  solid  medium  where,  as  already  stated,  the  re- 

FIG.  43. 


Total  reflexion. 


fracted  ray  constantly  approaches  the  axis  of  incidence 
has  alone  been  considered.  In  order  now  to  acquire 
a  knowledge  of  the  converse,  namely,  of  the  course 


62  OPTICS. 

taken  by  light  in  passing  from  water  in  to  air,  the  cubic 
glass  vessel  (fig.  43)  must  again  be  employed,  and  the 
little  mirror  B  which  receives  the  beam  of  light  directed 
vertically  downwards  by  the  mirror  A,  and  reflects  it 
upwards  against  the  surface  of  the  water,  must  be  placed 
beneath  the  surface  of  the  water.  The  beam,  when  it 
strikes  the  surface  of  the  water  at  M  from  below,  breaks  up 
into  a  reflected  beam  which  returns  through  the  water, 
and  into  a  refracted  beam  which  passes  out  into  the 
air.  This  last,  the  course  of  which  may  be  easily 
followed  both  by  the  illuminated  particles  of  dust  in  the 
air  and  by  the  spot  of  light  which  falls  on  the  lid  or  on 
the  opposite  wall,  runs  in  a  more  oblique  direction  than 
the  incident  beam  B  M.  A  beam  of  light  therefore 
passing  from  water  into  air  is  thus,  by  refraction,  de- 
flected from  the  perpendicular ;  in  fact,  as  may  readily 
be  demonstrated  by  measuring  the  angles,  it  follows 
a,n  exactly  inverse  path  to  a  ray  entering  water  from 
air.  Fig.  42  therefore  serves  to  exhibit  the  opposite 
course,  where  bn  is  the  ray  of  light  which  is  traversing 
the  water,  and  n  I  the  ray  refracted  as  it  emerges  into  the 
air.  r  will  of  course  then  be  the  angle  of  incidence, 
and  i  the  corresponding  angle  of  refraction ;  and  so  it 
appears  that  if  %  (or,  speaking  generally)  n  expresses 
the  refraction  that  light  undergoes  in  passing  from  air 

into  water  (or  any  other  transparent  substance)  j  (or    -  j 

represents  the  same  for  the  passage  from  water  (or  this 
other  substance)  into  air. 

By  rotating  the  mirror  B  the  ray  B  M  may  be  made 
to  strike  more  and  more  obliquely  against  the  surface  of 
the  water ;  the  emergent  ray  becomes  similarly  more 
and  more  deflected  from  the  perpendicular,  and  conse- 


REFRACTION.  63 

qnently  more  and  more  approximated  to  the  surface  of 
the  water.  It  is  not  difficult  in  this  way  to  make  the 
light  spot,  which  enables  us  to  follow  the  course  of  the 
emergent  ray,  strike  upon  the  wall  of  the  vessel  towards 
C  in  the  line  of  division  between  the  air  and  the  water. 
The  emergent  beam  now  passes  along  the  surface  of  the 
water,  and  its  angle  of  retraction  amounts  to  90°.  It 
cannot,  however,  be  refracted  through  an  angle  greater 
than  90°,  because  this  is  the  limit  of  the  possibility  of 
refraction.  Hence  if  the  beam  B  M  be  directed  still 
a  little  more  obliquely  to  the  surface  of  the  water,  no 
more  light  passes  out  into  the  air,  the  surface  of  the 
water  proving  absolutely  impenetrable  to  such  very 
obliquely  falling  rays.  It  may  at  the  same  time  be  re- 
marked that  at  the  moment  when  by  the  rotation  of  the 
mirror  B  the  limits  of  refraction  are  overstepped  and 
the  light  spot  at  C  at  the  surface  of  the  water  vanishes, 
the  ray  M D,  reflected  inwards,  which  up  to  this  time 
has  been  much  fainter  than  the  incident  ray  B  M, 
suddenly  gains  in  intensity  and  becomes  just  as  bright 
as  the  incident  ray.  This  is  due  to  the  circumstance 
that  the  light  of  the  beam  B  M,  being  no  longer  divided 
into  a  reflected  and  a  refracted  portion,  the  latter  is 
added  without  loss  to  the  former,  and  the  beam  is  said 
to  undergo  total  reflexion.  The  angle  of  incidence  at 
which  refraction  ceases  and  total  reflexion  commences 
is  termed  the  critical  angle.  This  amounts  in  the 
case  of  water  to  48°  35',  for  glass  to  40°  49',  and  for  the 
diamond  to  23°  43".  A  surface  at  which  total  reflexion 
occurs  constitutes  the  most  perfect  mirror  we  possess. 
And  now  let  a  glass  prism  (fig.  44)  which  in  section  forms 
a  right-angled  triangle  with  equal  sides,  be  placed  in  the 
beam  of  light  coming  from  the  Heliostat.  The  rays  which 
6 


64  OPTICS. 

fall  perpendicularly  upon  the  kathetal  surface  A  C,  pass 
without  deflection  through  the  glass  and  strike  at  an 
angle  of  45°  (which  is  consequently  larger  than  the 
critical  angle  of  glass,  equal  to  40°  49')  upon  the  sur- 
face of  the  Hypothenuse  A  B.  They  are  here  totally 
reflected,  without  even  a  trace  of  light  entering  the  air 

behind  A  B,   ar.d  pass   without 
FIG-44-  farther   deflection  through  the 

second  kathetal  surface  B  C.  To 
the  eye  above,  the  beam  on  its 
emergence  is  not  sensibly  fainter 
than  on  its  entrance,  and  it 
does  actually  contain  about  92 
per  cent,  of  the  original  amount 
of  light,  the  loss  of  8  per  cent. 
Totally  reflecung  prism.  being  due  to  partial  reflexion 
taking  place  at  the  surfaces  of 

entrance  and  emergence.  The  best  silvered  mirrors 
reflect  90  per  cent,  mercury  itself  only  60  per  cent,  and 
a  polished  glass  surface  only  4  per  cent,  of  the  incident 
light. 

33.  A  luminous  point  situated  beneath  the  surface  of 
the  water,  or  more  generally  beneath  the  surface  of  any 
transparent  medium,  in  consequence  of  refraction,  is 
seen,  not  in  the  position  it  actually  occupies,  but  in  a 
higher  position.  Fig.  45  shows  how  the  rays  proceed- 
ing to  the  eye  from  the  point  A  appear  to  come  from 
the  point  A',  which  is  consequently  to  be  regarded  as 
a  virtual  image  of  the  point  A.  The  depth  of  the  point 
A'  below  the  surface,  providing  the  rays  do  rot 
emerge  very  obliquely,  is  the  nth  part  of  the  actual 
depth  of  the  point  A,  n  being  regarded  as  the  index  of 
refraction  of  light  in  passing  from  air  into  the  trans- 


REFRACTION. 


65 


parent  medium  in  question.  In  water,  for  example, 
all  objects  appear  to  be  about  one  quarter  less  deep, 
hence  it  comes  to  pass  that  any  mass  of  water  the 
bottom  of  which  can  be  seen,  appears  to  be  less  deep 


FIG.  45. 


FIG.  4o. 


Apparent  position  of  a  point  situated 
beneath  the  surface  cf  the  water. 


Appearance  presented  by  a  rod  dipped  in 
water. 


FIG.  47. 


than  it  really  is.  For  the  same  reason  the  portion  of 
a  perpendicular  post  which  is  under  water  appears  to 
be  shortened,  and  a  rod  held  obliquely  in  the  water  to 
be  bent  at  the  point  of  immersion  (fig.  46). 

When  the   hand   is   dipped  in  water,  or   a  coin  is 
looked  at  from  above,  it  appears  to  be  slightly  enlarged, 
because    it   appears    to  be  brought 
.nearer  to  the  eye,  and  is  therefore 
seen  under  a  larger  angle. 

34.  A  ray  of  light  in  passing  from 
the  air,  A  A  (fig.  47)  into  a  trans- 
parent medium,  7?  B,  and  again  em- 
erging into  air  (A  A)  on  the  other 
side  of  the  medium,  undergoes  re- 
fraction both  at  the  point  of  entrance 
and  at  that  of  emergence.  If  the 
ray  passes  through  a  plate  bounded 
by  parallel  surfaces,  it  becomes,  as  is  shown  in  fig.  47, 
approximated  to  the  axis  cf  incidence  at  the  point  of 


m 

A 


Refraction  through  a  trans- 
parent plate  with  parallel 
surfaces. 


ti6  OPTICS. 

entrance,  and  diverted  from  it  to  the  same  extent  a{ 
tiie  point  of  emergence.  The  emergent  ray  consequently 
pursues  its  course  parallel  to  the  entering  ray,  though 
without  forming  its  direct  continuation.  The  only  change 
it  undergoes  from  its  original  direction  is  a  lateral  shift- 
ing, which  is  greater  in  amount  the  more  obliquely  the 
ray  strikes  the  plate,  the  thicker  the  plate,  and  the 
greater  its  index  of  refraction.  Thin  plates,  as  for 
example  the  ordinary  panes  of  glass  in  our  windows, 
produce  so  slight  a  shifting  that  objects  are  seen  through 
them  of  their  ordinary  size  and  shape,  and  in  their 
natural  position.  That  a  ray  of  light,  after  its  passage 
through  a  plate  with  parallel  surfaces  continues  to  pass 
in  a  direction  parallel  to  its  original  direction,  and  only 
undergoes  a  lateral  shifting,  may  be  easily  demonstrated 
by  a  simple  experiment.  If  a  thick  plate  of  ordinary  glass 
be  held  in  a  beam  of  light  proceeding  from  the  mirror 
of  the  Heliostat  so  that  about  half  the  beam  passes 
without  obstruction  at  the  side  of  the  plate  whilst  the 
other  half  is  refracted  through  it,  it  will  be  seen  thai 
the  latter  portion  continues  parallel  to  the  former  and 
throws  a  light  upon  a  screen  placed  opposite  to  it,  which 
is  more  distant  from  the  light  thrown  by  the  direct  rays 
in  proportion  as  the  rays  are  made  to  strike  the  plate 
more  obliquely.  Let  a  second  plate  of  flint  glass  be  now 
placed  upon  the  first  plate  ;  the  lateral  shifting  increases, 
jut  the  emergent  rays  still  always  remain  parallel  to 
the  entering  rays,  nor  is  any  change  in  the  parallelism 
produced  if  a  third  plate  be  added.  However  numerous 
may  be  the  transparent  plates  of  different  substance? 
superimposed  on  each  other,  the  rays  on  their  emer- 
gence into  the  air  remain  parallel  to  their  course  in  the 
*ir  before  their  entrance  into  the  transparent  medium. 


INFRACTION. 


67 


Now  since  in  the  passage  of  a  ray  of  light  through 
the  two  plates  A  and  B  (fig.  48)  the  angle  of  emergence 
i'  is  equal  to  the  angle  of  incidence  i,  the  refracted  ray 
must  pursue  the  same  course  in  the  medium  B  which  it 
would  have  had  if  this  medium  had  been  struck  directly 
by  the  incident  ray  passing  in  the  direction  i,  alter 

FIG.  48 


W 


B 


Refraction  through  two  parallel  plates. 

removal  of  the  plate  A.  The  plate  A  therefore  exerts  no 
influence  upon  the  direction  of  the  rays  of  light  in  the 
medium  B.  It  is  now  obvious  that  in  the  experiment 
described  in  §  30,  the  glass  plate  (a  6,  fig.  41)  through 
which  the  rays  must  pass  before  they  penetrate  into  the 
interior  of  the  vessel,  does  not  interfere  with  the  re- 
sult because  it  does  not  cause  any  alteration  in  the 
direction  of  the  refracted  ray. 

From  the  circumstance  that  a  pencil  of  light  in 
traversing  two  or  more  parallel  plates  undergoes  no 
change  in  direction,  it  is  moreover  legitimate  to  con- 
clude *  that  the  index  of  refraction  of  a  pencil  of 
light  in  passing  from  one  medium,  A,  into  a  second 


See  Appendix  to  this  Chapter. 


FIG.  49. 


68  OPTICS. 

nf 

medium,  B,  may  be  expressed  by  the  quotient       ,  where 

n 

n"  represents  the  index  of  refraction  of  the  medium  B, 
and  n  that  of  A  in  relation  to  the  air.  Thus,  for  example, 
the  index  of  refraction  from  water  into  glass  =  -.-  — 

=  1-148. 

35.  When  a  beam  of  light  traverses  a  transparent 
body,  the  opposite  surfaces  of  which  are  inclined  to  one 
another,  the  emerging  ray  no  longer  remains  parallel 
to  the  incident,  but  is  diverted  from  its  original  direc- 
tion, and  fig.  49  shows  the  course 
of  the  beam  under  these  circum- 
stances. A  straight  triangular  prism 
of  glass  (fig.  50)  may  be  used  for 
experiments  on  this  mode  of  deflec- 
tion. When  the  surfaces  abed  and 
a  b  gf  are  used  as  surfaces  of  en- 
trance and  emergence,  the  edge,  a  6, 
in  which  these  two  surfaces  meet 

Refraction  through  a  pieoe  of     .  n     , ,  «         ,  .  -.  -, 

glass  the  surfaces  of  which  is  termed  the  retracting  edge,  and 

are  not  parallel.  -i          -»         /•         i  1 1 

the  angle,  a  a  /,  where  they  meet, 
the   refracting  angle  of  the  prism.     All  planes   which, 
like   the  terminal  surfaces    daf  and    cbg,    or  planes 
parallel  to  them,  are  perpendicular  to  the 
refracting  edge,  are  termed  chief  or  prin- 
cipal sections  or  planes  of  the  prism,    arid 
the  remarks  here  made  will  be  limited  to 
those  rays  which  run  in  principal  sections. 
If  the  opening    of  the    Heliostat    be 
closed  with  a  red  glass,*  and  a  prism  (fig. 

A  prism.  r 

51)  with  vertically-placed  refracting  edge 
oe  brought  in  the  path  of  the  horizontal  red  pencil   of' 

*  The  object  of  this  proceeding  will  be  presently  explained. 


REFRACTION.  69 

light,  so  that  about  one  half  of  the  rays  passing  by  the 
side  of  the  edge,  A,  pursue  their  original  direction, 
A  D,  whilst  the  other  half  are  refracted  by  the  prism 
and  deflected  towards  A  E ;  the  amount  of  deflection, 
that  is  to  say,  the  size  of  the  angle  DAE  between  the 
emergent  and  the  direct  rays,  will  be  found  to  vary  as 
the  position  of  the  prism  in  regard  to  the  incident  rays, 


Deflection  througli  a  prism. 

or,  which  comes  to  the  same  thing,  as  the  direction  of 
the  rays  in  relation  to  the  prism  is  altered. 

On  rotating  the  prism  to  a  greater  or  less  extent, 
a  position  may  easily  be  discovered  in  which  the  deflec- 
tion is  less  than  in  any  other  position.  As  it  is  turned 
away  from  this  position  in  either  direction,  or,  which 
expresses  the  same  thing  in  other  words,  as  the  rays 
are  made  to  fall  more  or  less  obliquely  upon  the  prism 
than  in  the  position  of  least  deflection,  the  deflection 
becomes  constantly  more  and  more  marked. 

In  order  to  determine  the  course  pursued  by  a  raj 
of  light  with  the  least  deflection,  the  following  experi- 
ment may  be  made.  A  part  of  the  incident  light  is 
reflected  at  the  anterior  surface,  A  B,  of  the  prism, 
towards  M F.  The  half  of  the  angle,  S  MF,  is  conse- 
quently the  incident  angle.  If  a  small  mirror  be 
placed  at  E,  perpendicularly  to  the  emergent  rays, 


70  OPTICS. 

these  are  reflected  back  upon  themselves,  and  are  re- 
flected at  the  posterior  surface,  A  C,  of  the  prism, 
towards  NGj  then  the  half  of  the  angle  EN G  is  the 
emergent  angle.  It  may  now  be  easily  shown  by 
direct  measurement  that  if  the  prism  be  placed  in 
the  position  of  least  deflection,  the  angle  8  M  F  is  equal 
to  the  angle  E  A7  G,  or  that  the  angle  of  entrance  and 
of  emergence  are  equal  to  each  other.  But  if  the  inci- 
dent and  the  emergent  rays  form  equal  angles  with  the 
surfaces  of  the  prism,  the  refracted  ray  M N,  in  its 
course  through  the  prism,  must  be  equally  inclined  to 
both  surfaces.  The  minimum  deflection  occurs  therefore 
when  the  ray  in  the  interior  of  the  prism  forms  equal  angles 
with  the  surfaces  of  entrance  and  of  emergence.  The 
knowledge  of  the  minimum  deflection  of  a  prism  is  a 
matter  of  great  importance  in  practical  optics,  because 
we  are  able  from  it  and  the  refracting  angle  of  the  prism 
to  determine  with  great  exactness  the  index  of  refrac- 
tion of  the  substance  of  which  it  is  composed. 

From  fig,  52.  which  represents  the  coarse  of  a  ray 

FIG.  52. 


Smallest  deflection  through  a  prism. 


of  light  in  the  case  of  least  deflection,  it  results*  that 
the  angle  of  refraction,  r,  is  equal  to  half  the  angle  of 

*  See  Appendix  to  this  Chapter. 


REFRACTION.  71 

the  prism  5,  and  the  angle  of  incidence,  i,  is  equal  to 
half  the  combined  minimum  deflection  and  prism  angle. 

If,  however,  the  angle  of  refraction  belonging  to 
the  angle  of  incidence,  vbe  known,  the  index  of  refrac- 
tion must,  in  accordance  with  the  law  of  refraction,  be 
equal  to  the  ratio  between  the  sines  of  these  two  angles. 

In  order  to  obtain  the  index  of  refraction  of  a  body, 
the  following  method  is  adopted.  A  prism  of  the  sub- 
stance is  prepared,  the  refracting  angle  of  which  is 
measured  by  the  reflecting  Goniometer  (§  19),  and  the 
minimum  deflection  is  determined  when,  by  testing, 
it  has  been  brought  into  the  right  position.  From 
these  two  data,  which  can  be  ascertained  with  great 
accuracy,  the  index  of  refraction  can  be  easily  deduced 
by  the  above  method. 

In  order  to  give  to  a  fluid  the  form  of  a  prism  it  is 
introduced  into  a  vessel  in  which 
the  opposite  inclined  walls  are  FIG.  53. 

made  of  plates  of  glass,  care- 
fully ground  to  plane  surfaces. 
Fig.  53  is  such  a  hollow  prism. 
As  plates  with  parallel  surfaces 
do  not  alter  the  direction  of  the 
rays  of  light,  they  do  not  inter- 
fere with  the  measurement  of 
the  deflection  caused  by  the  Hoiiow  prism. 

fluid. 

The  indices  of  refraction  given  above  (§  31)  were  all 
obtained  in  this  manner. 

36.  When  a  comparison  is  made  of  several  prisms 
composed  of  the  same  kind  of  glass,  the  refracting  angles 
of  which  differ,  it  is  found  that  the  minimum  deflec- 
tion increases  more  quickly  than  the  refracting  angle. 
Thus  for  prisms  of  ordinary  glass  it  appears  that, 


72  orTJcs. 

When  the  left-acting  angle  amounts  to  20°,  the  mini- 
mum deflection  amounts  to  10°  49'. 
When  the  refracting  angle  amounts  to  40°,  the  mini- 
mum deflection  amounts  to  23°  6". 
When  the  refracting  angle  amounts  to  60°,  the  mini- 
mum deflection  amounts  to  39°  49'. 
It  is  only  in   the  case  of   prisms  with   very  small 
refracting  angles  that  the  deflection  holds   the  same 
ratio,  for  it  is  found  that 

With  a  refracting  angle  of  2°  the  minimum  deflection 

is  1°  3f . 
With  a  refracting  angle  of  4C  the  minimum  deflection 

is  2°  7*'. 
With  a  refracting  angle  of  6°  the  minimum  deflection 

is  3°  11'. 

The  amount  of  refraction  in  thin  acute-angled  prisms 
does  not  alter  materially  even  if  the  incident  ray  is  in- 
clined several  degrees  to  that  which  traverses  the  prism 
under  equal  angles.  For  example,  the  prism  of  4°  may 
be  moved  as  much  as  5°  to  one  side  or  the  other  from 
the  position  of  minimum  refraction,  or  may  thus  be 
rotated  10°  without  the  deflection  varying  more  than  a 
minute. 

It  may  therefore  be  laid  down  that  a  prism  with  very 
small  refracting  angle,  as  long  as  the  rays  do  not  fall  too 
obliquel}'  upon  it,  invariably  produces  an  amount  of  deflec* 
tion  proportional  to  the  refracting  angle. 


REFRACTION. 


73 


APPENDIX  TO  CHAPTER  V. 

To  §  §  31  and  32.  By  means  of  the  law  of  refraction  the  angle 
of  refraction  corresponding  to  each  angle  of  incidence  (and  the 
converse;  may  be  easily  determined  either  by  calculation  or  by 
construction.  The  latter  may  be  conducted  in  the  mode  indicated 
in  fig.  42.  The  construction  shown  in  fig.  54  is  still  more  con- 
venient. Two  circles  are  described  around  the  point  of  incidence 
in  the  plane  of  refraction,  one  of  them  with  a  radius  =  1,  the 
other  with  the  radius=n,  n  being  the  index  of  refraction  of  the  ray 
in  passing  out  of  the  first  into  the  second  medium.  Now  let  the 
incident  ray  /  n  be  prolonged  to  intersect  the  first  circle  in  the 

FTO.  54. 


Construction  of  the  refracted  ray. 

point  m,  and  through  m  drawn  p  m  q  parallel  to  the  axis  of  in- 
cidence, intersecting  the  second  circle  in  the  point  p,  then  n  p 
is  the  direction  of  the  refracted  ray.  For  since  the  angle  q  m  n 
is  equal  to  the  angle  of  incidence  i,  the  sin  i  =  q  n  ;  and  further, 
since  the  angle  qpn  is  equal  to  the  angle  r,  n  sin  r  =  qn,  and 
hence  as  is  required  by  the  law  of  refraction, 

sin  i  =  n  sin  r. 

For  any  ray  p  n  proceeding  from  the  second  medium,  let  a  line 
parallel  to  the  axis  of  incidence  be  drawn  through  p  to  cut  the 


74  OPTICS. 

first  circle  at  the  point  m,  then  the  line  m  .*>,  produced,  gives  the 
direction  of  the  emerging  ray  n  I. 

The  last  construction  becomes  impossible  when  as  in  the  ray 
?  n  the  parallel  to  the  axis  of  incidence  no  longer  cuts  the  first 
circle.  The  total  reflexion  which  this  ray  experiences  is  thus 
rendered  intelligible. 

If  the  parallel  touches  the  first  circle  just  at  the  end  of  its 
horizontal  diameter,  as  occurs  with  the  ray  t  n,  the  refracted  ray 
passes  out  towards  n  q  along  the  limiting  surfaces  of  the  two 
media,  and  t  n  k!  =  y  is  the  critical  angle.  The  ratio  thus  holds, 
as  appears  Irom  the  construction 

n  sin  y  =  1 ,  or  sin  y  =  -  . 
n 

To  §  34.  That  the  index  of  refraction  in  passing  from  a 
medium  A  into  a  second  medium  J5,  is  equal  to  the  quotient 

n~ ,  where  n'  represents  the  index  of  refraction  of  the  medium  A, 

n"  that  of  the  medium  B,  as  compared  with  air,  can  be  demon- 
strated in  the  following  manner.  In  fig.  55,  which  represents 

FIG.  55. 


Refraction  through  two  parallel  plates. 

the  passage  of  a  ray  of  light  through  two  parallel  plates,  we 
have  on  entrance  into  the  first  plate 

sin  i  =  n'  sin  r, 


KEFKACTION.  75 

and  on  emergence  of  the  ray  from  the  second  plate  into  th?  air 
sin  i'  =  n"  sin  r'. 

But  inasmuch  as  the  emergent  ray  is  parallel  to  the  incident 
ray,  i  =  i'  consequently  also,  sin  t  =  sin  zv,  and 

n'  sin  r  =  n"  sin  r1 
or 

»"     •    ^ 
sin  r  =  — 7  sin  r. 

n' 

In  the  transition  of  the  ray  from  the  first  into  the  second  plate,  r 
is  obviously  the  angle  of  incidence,  and  r'  the  angle  of  refraction, 

n" 
and  consequently   —  is  the  ratio  of  refraction  corresponding  to 

this  transition. 

To  §  35.  The  deflection  of  the  incident  ray  caused  by  a  prism 
placed  in  any  given  position  amounts  to  the  sum  of  the  deflection 
on  entrance  and  the  deflection  on  emergence.  If  t  and  i'  ( fig. 
56)  indicate  the  angles  which  the  incident  and  the  emergent 
ray,  and  r  and  r'  the  angles  which  the  ray  in  its  course 
through  the  prism  makes  with  the  axis  o£  incidence,  then  i—r  is 
the  amount  of  deflection  in  the  first,  and  i'  —  r1  that  in  the  second 
refraction.  The  total  deflection,  D,  as  appears  from  the  figure, 
is  the  sum  of  the  two  separate  deflections,  so  that 

D  —  i  —  r  +  i',  —  r'  or  D  =  i  +  i'  —  (r  +  r'). 

From  the  figure  it  may  also  be  concluded  that  the  sum  of  the 
two  angles  o  refraction  remains  constantly  equal  to  the  refracting 
angle  of  the  prism  b,  or  that  constantly 

r  +  r>  =  b. 

Consequently  the  deflection  may  also  be  expressed  in  the  follow- 
ing form  : — 

D  =  i  +  if  -  b. 

When  in  the  case  of  the  minimum  refractior  (c?,  fig.  52),  t  =  r, 
and  r  =  r',  we  obtain 

2r  =  b  and  d  =  2i  —  b. 
Thence  it  results   that  the  angle   of  incidence   i  =  ^  (d  +  ft), 


76  OPTICS. 

and  the  angle  of  refraction  r  —  ^  b.  We  obtain  therefore  for  the 
calculation  of  the  index  of  refraction  the  equation 

sin  i  (d  -f  b} 

~    jan  j.  b.  ~ 

That  the  minimum  of  deflection  occurs  with  equiangular  transit, 
i.e.  when  the  ray  of  light  makes  equal  angles  with  the  two  sides 
of  the  prism,  may  be  shown  by  the  following  statement : — We 
consider  that  the  course  of  any  ray  of  light  in  the  prism 
is  as  in  fig.  56,  from  left  to  right  and  upwards;  we  compare 

FIG.  66. 


Passage  of  a  ray  of  light  through  a  prism. 

with  this  a  second  ray,  which  runs  with  equal  inclination  to 
the  two  surfaces  from  the  left  to  right,  and  downwards ;  these 
two  rays  lie  symmetrically  with  regard  to  the  equiangular  ray 
of  fig.  52,  and  undergo,  since  they  only  in  this  respect  differ  from 
one  another,  that  i  and  zv,  and  also  r  and  r',  are  interchanged, 
equal  amounts  of  deflection.  It  may  now  be  easily  shown  that 
the  amount  of  deflection  of  the  non-equiangular  ray  of  fig,  56 
is  greater  than  that  of  the  equiangular  ray  of  fig.  52. 

The  angle  r  in  fig.  56  is  greater  than  with  equiangular  rays, 
the  angle  r'  on  the  other  hand  is  just  as  much  smaller,  since 
the  sum  of  r "+  r'  =  b.  If  we  proceed  consequently  from 
equiangular  to  non-equiangular  rays  the  angle  i  augments,  whilst 
i'  diminishes.  By  means  of  the  construction  fig.  54  it  may  easily 
be  demonstrated  that  if  the  angle  of  refraction  r  be  allowed  to 
increase  and  diminish  about  equally,  the  increase  of  the  angle  of 
incidence  z  is  in  the  former  case  greater  than  is  its  diminution  in 


REFRACTION.  77 

the  latter.  In  the  transition  from  equiangular  to  any  other  raya 
consequently,  in  the  expression 

D  =  i+  i'  -  b, 

the  angle  «  augments  30  much  the  more  as  the  others  diminish  : 
that  is  to  say,  the  deflection  of  the  ray  becomes  greater,  or  which 
is  the  same  thing,  the  minimum  deflection  occurs  with  equiangular 
transit. 

To  §  36.  The  proposition  laid  down  in  §  36  in  regard  to 
acute-angled  prisms  may  be  easily  established  theoretically.  If 
for  example  the  refracting  angle  of  a  prism  be  very  small,  those 
rays  which  are  near  to  the  minimum  deflection  deviate  but  little 
from  the  axis  of  incidence.  Here,  therefore,  only  very  small 
angles  of  incidence  and  emergence  are  dealt  with,  to  which  the 
simplified  law  of  refraction  applies  (see  end  of  §  31),  from  which  it 
appears  that 

i  =  7?,?*  and  i'  =  nr1 
and  the  deflection 

D  =  n  (r  +  r')  -  (r  +  r')  =  (n  -  1)  (r  +  r>) 

or  because 

r  +  r'  =.  b, 

Z)=(n-  1)  b, 

that  is  to  say,  the  deflection,  whatever  may  be  the  angle  of  inci- 
dence, providing  only  that  it  remains  very  small,  is  determined 
exclusively  by  the  index  of  refraction  and  the  refracting  angle 
of  the  prism,  and  indeed  is  proportional  to  this  last. 


OPTICS. 


CHAPTER  VI. 

LENSES.      — 


37.  X*HN  pieces  of  glass,  the  two  surfaces  of  which 
(or  one  surface,  the  other  remaining  flat)  have  been 
ground  to  a  spherical  form,  are  termed  lenses. 

Convex  lenses  are  those  which  are  thicker  in  the 
middle  than  at  the  edge.  Fig.  57  exhibits  three  different 
forms,  as  seen  in  section,  namely,  a  a  bi- convex,  b  a 
plano-convex,  and  c  a  concavo-convex  lens. 


FIG.  57. 


FIG.  58. 


I  c 

Convex  lenses. 


a  b  c 

Concave  lenses. 


Concave  lenses  (fig.  58)  are  thicker  at  the  edges 
than  in  the  middle :  a  is  a  bi-concave,  b  a  plano-concave, 
and  c  a  convexo-concave  lens. 

The  term  axis  of  a  lens  indicates  the  straight 
line  which  joins  the  centres  C  and  C'  (fig.  59),  of  the 
two  spheres  of  which  the  limiting  surfaces  are  segments. 
Where  one  of  the  surfaces  is  flat,  a  line  drawn  perpen- 
dicularly to  that  surface  from  the  centre  of  curvature  of 


LENSES.  79 

the  curved  surface  is  regarded  as  the  axis.  The  form 
of  a  lens  is  symmetrical  around  its  axis,  for  all  planes 
passing  through  the  axis,  which  are  termed  chief  or  prin- 
cipal planes  or  sections,  have  the  same  sectional  outline. 
The  angle  A  C  B  (fig.  59)  which  two  straight  lines, 
drawn  to  diametrically  opposite  points  of  the  border  of 


B 

Axis  and  centres  of  curvature. 

the  lens  from  the  centre  of  curvature,  make  with  one 
another,  is  termed  the  aperture  of  the  corresponding 
surface  of  the  lens.  We  shall  here  only  have  to  do 
with  such  lenses  as  have  a  small  aperture  not  exceeding 
six  or  eight  degrees  at  most. 

38.  If  a  pencil  of  parallel  rays  from  the  sun  be 
directed  upon  a  bi-convex  lens  (fig.  60),  parallel  with 
its  axis,  these  will  be  so  refracted  that  they  will  all  pass 
through  one  and  the  same  point,  F,  situated  on  the 
axis  on  the  other  side  of  the  lens,  which  is  called  the 
focus. 

If  the  several  rays  be  followed  in  their  passage 
through  the  lens  it  is  observable  that  each  is  refracted  in 
exactly  the  same  mode  as  in  a  prism  whose  refracting 
angle  is  turned  away  from  the  lenticular  axis,  with  this 
difference,  however,  that  for  each  ray  there  is  a  diffe- 
rent refracting  angle.  The  small  angle  between  the 
directions  of  the  two  lenticular  surfaces  at  the  points 
of  entrance  and  emergence  of  the  ray  in  question  is  to 


80  OPTICS. 

be  regarded  as  the  refracting  angle.  This  angle  is 
proportionally  greater  as  we  recede  from  the  axis  of  the 
lens.*  The  lens  acts  just  as  if  each  raj  struck  an 
acute-angled  prism,  the  refracting  angle  of  which  is 


Focal  point. 

greater  in  proportion  as  the  point  of  incidence  is  further 
from  the  axis. 

If  what  has  been  said  above  in  regard  to  the  relation 
of  acute-angled  prisms  be  remembered,  it  may  be  con- 
ceived that  rays  pursuing  a  parallel  course  on  this 
side  of  the  lens,  the  further  they  severally  strike  the 
lens  from  its  axis,  musl?  run  together  on  the  other  side°\ 
of  the  lens  into  one  and  the  same  point  of  the  axis. 
The  ray  which  runs  in  the  axis  itself  meets  parallel 
surfaces  upon  its  entrance  and  emergence  from  the 
lens,  and  therefore  experiences  no  deflection. 

On  the  supposition  that  the  rays  fall  parallel  upon  the 
surface  of  the  lens  from  the  side  towards  F,  their  union 
will  then  occur  on  the  other  side  of  the  lens  in  a  point 
of  the  axis  which  will  also  be  at  the  same  distance  from 
the  lens  as  the  point  F,  because  the  rays  will  meet  the 
same  refracting  angles  at  the  same  distance  from  the 
axis,  and  will  consequently  experience  the  same  de- 
flection as  before.  Every  lens  therefore  possesses  two 
focal  points  upon  its  axis,  which  are  placed  on  opposite 
sides  of  it,  at  the  same  focal  distance. 

*  See  Appendix  to  Miis  Chapter. 


LENSES.  81 

39.  The  flame  of  an  electric  lamp  is  now  to  be 
brought  into  the  focus  F  (fig.  60)  of  the  lens.  The  result 
may  be  predicted.  A  beam  of  light,  composed  of  rays 
running  parallel  to  the  axis,  emerges  on  the  other  side 
of  the  lens.  Following  the  plan  previously  adopted,  it 
may  be  said  that  rays  proceeding  from  the  focus  on  one 
side  of  the  lens  run  on  the  other  side  towards  an  in- 
finitely remote  point  of  the  axis. 

If  the  light  from  the  lens  be  now  removed  till  it 
reaches  the  point  R  (fig.  61),  a  cone  of  rays  may  be  seen 
to  emerge  which  converge  towards  a  point  8  on  the  axis. 
This  point  8,  in  which  all  the  rays  proceeding  from  R 
that  fall  upon  the  lens  unite,  is  the  real  image  of  the 
luminous  point  R. 

When  the  luminous  point  R  (fig.  62)  is  brought  to 
exactly  double  the  focal  distance  from  the  lens,  its  image, 
8,  on  the  other  side,  will  be  double  the  focal  distance 
from  the  lens  also. 

When  the  luminous  point  is  placed  at  8  (fig.  61)  its 
image  is  formed  at  the  point  R,  which  was  before  the 

FIG.  61. 


Conjugate  foci. 

position  of  the  light.  The  points  R  and  8  are  conse- 
quently so  associated,  that  the  one  is  the  image  of  the 
other,  and  they  are  said  to  be  conjugate  to  each  other. 
W^hen  one  is  more  than  double  the  focal  distance  from 
the  lens,  the  other  is  less  upon  the  opposite  side,  but 


82 


OPTICS. 


always  at  a  greater  distance  from  it  than  the  simple  focal 
distance. 


If  the  luminous  point  T  (fig.  63)  be  situated  between 
the  focus  and  the  lens,  this  no  longer  has  the  power  of 


making  the  strongly  divergent  rays  parallel  or  con- 
vergent, but  simply  diminishes  their  divergence.  An 
actual  union  of  the  refracted  rays  can  now  no  longer 
take  place,  but  if  prolonged  backwards,  they  pass 
through  a  point  F,  situated  upon  the  axis  on  the  other 
side  of  the  lens,  which  is  more  remote  from  the  lens 
than  the  luminous  point  T;  in  other  words,  the  rays 
emanating  from  T  proceed  divergingly  after  having 
traversed  the  lens,  just  as  if  they  emanated  from  the 
point  F.  The  point  F  is  consequently  the  virtual  image 
of  the  point  T. 

If,  conversely,  a  converging  pencil  of  rays  proceed- 
ing from  the  right  side  (fig.  63),  fall  upon  the  lens 
which  is  directed  to  the  virtual  luminous  point  F,  the 


LENSES.  85 

rays  are  made  to  unite  at  the  real  image-point  T.  The 
points  T  and  F  therefore  constitute  image-points  of 
each  other,  and  they  also  are  consequently  termed 
conjugate  points. 

40.  The  behaviour  of  lenses,  in  regard  to  light, 
which  has  just  been  described,  is  easily  explained  by  the 
peculiarity  that  prisms  with  small  refracting  angle 
possess  of  deflecting  equally  all  rays,  whatever  may  be 
their  direction,  providing  they  do  not  fall  too  obliquely 
upon  them.  In  consequence  of  this  peculiarity,  all  rays 
which  are  not  inclined  to  the  axis  at  too  great  an 
angle  must  undergo  the  same  deflection  at  one  and  the 
same  point  of  the  lens.  The  ray  R  A,  for  example  (fig. 
61),  striking  near  the  edge  of  the  lens,  inasmuch  as  it 
is  refracted  towards  A  S,  undergoes  the  same  deflection 
which  the  ray  A  N,  running  parallel  to  the  axis,  expe- 
riences ;  that  is  to  say,  the  angle  R  A  8,  wherever  the 
luminous  point  R  may  be,  is  always  equal  to  the  angle 
F  A  N,  the  magnitude  of  which  is  given,  once  for  all, 
with  the  focal  distance.  The  conjugate  points  may  be 
very  easily  determined  by  construction;  if  the  angle 
F  A  N  be  cut  out  of  a  piece  of  cardboard,  and  having 
been  placed  with  its  apex  upon  the  point  A  and  rotated 
around  this  point,  the  sides  containing  the  angle  T  then 
always  cut  the  axis  in  two  points  conjugate  to  each 
other. 

It  results  as  a  necessary  consequence  from  the  above- 
mentioned  proposition,  according  to  which  in  lenses  of 
small  aperture  the  deflection  of  a  ray  is  greater  in  pro- 
portion as  the  part  of  the  lens  which  it  strikes  is  further 
from  the  axis,  that  all  rays  proceeding  from  any  point 
on  the  axis  pass  again  after  refraction  through  some 
point  of  the  axis. 


84  OPTICS. 

41.  The  concordance  which  exists  between  the 
properties  of  convex  lenses,  so  far  as  we  have  at  present 
gone,  and  those  of  concave  mirrors,  is  so  remarkable 
that  it  is  scarcely  necessary  that  they  should  be  expressly 
pointed  out.  And  it  will  not  be  surprising  if  in  the 
course  of  the  following  researches  results  are  obtained 
essentially  agreeing  with  those  already  given  in  the 
case  of  concave  mirrors. 

If,  for  example,  I  place  the  light  of  an  electric 
lamp  at  a  (fig.  64)  above  the  axis,  its  image  is  formed 

FIG.  64. 


Production  of  a  real  image. 

below  the  axis  in  A.  An  imaginary  straight  line  join- 
ing the  points  a  and  A  passes  through  the  centre  0  of 
the  lens,  and  a  ray  striking  the  lens  in  this  direction 
(a  0)  undergoes  no  deflection,  because  it  meets  parallel 
portions  of  the  surface  of  the  lens.  It  behaves  itself 
consequently  like  a  ray  running  in  the  axis  itself.  The 
term  secondary  axis  has  therefore  been  applied  to  every 
line  passing  through  the  centre  of  the  lens,  in  order  to 
distinguish  such  lines  from  the  chief  axis  which  joins 
the  centres  of  the  two  spheres  of  which  the  surfaces  of 
curvature  are  segments.  The  same  laws  hold  in  regard 
to  each  secondary  axis  for  rays  that  do  not  fall  too 
obliquely,  as  has  already  been  stated  as  applying  to 
the  chief  axis.  A  pencil  of  rays,  for  example,  which 
falls  upon  the  lens  parallel  to  its  secondary  axis  a  0. 


LENSES.  85 

will  be  united  in  a  point  upon  this  secondary  axis  at 
about  the  focal  distance  of  the  lens  0  F.  Every  secon- 
dary axis  consequently  also  possesses  two  focal  points, 
and  its  conjugate  points  are  in  all  respects  similar  to 
those  of  the  chief  axis. 

42.  If  from  the  points  a  and  A,  which  correspond  as 
light  object-point  and  image- point  on  the  secondary  axis 
a  0  A,  we  let  fall  the  lines  a  b  and  A  B  perpendicular  to 
the  principal  axis,  so  that  each  is  bisected  by  the  chief 
axis,  the  points  b  and  B  upon  the  secondary  axis,  b  o  B, 
are  obviously  also  conjugate  to  each  other.  So  long  as  the 
angle  between  the  secondary  axis  a  0  and  the  principal 
axis  is  very  small,  all  points  of  the  line  a  b  may  b6  re- 
garded as  equally  remote  from  the  middle  of  the  tens  0, 
and  likewise  all  points  of  the  line  A  B.  Every  point  of 
the  line  a  b  has  therefore  its  conjugate  point  upon  the 
line  A  B,  which  is  at  the  spot  where  these  are  struck  by 
their  own  axis.  The  middle  points  of  a  b  and  A  B,  for 
example,  are  conjugate  points  upon  the  chief  axis. 

From  the  preceding  illustration,  which  is  limited  to 
the  plane  of  the  construction,  a  more  general  statement 
affecting  the  space  around  the  chief  axis  can  easily  be 
deduced.  If,  for  instance,  the  vertical  planes  a  b  and  A  B 
be  conceived  to  be  placed  at  two  conjugate  points  of  the  chief 
axis,  each  point  of  the  one  plane  will  have  its  image  in  the 
other  plane  at  the  spot  where  this  is  struck  by  the  axis  cor- 
responding to  each  point.  The  two  planes  are  said  to  be 
'  conjugate  to  each  other.'  If  therefore  any  line  be 
situated  in  the  one  plane,  there  is  projected  from  the 
lens  an  exact  image  of  it  upon  the  other  conjugate 
plane,  the  size  of  which  is  in  the  same  proportion  as 
their  relative  distances  from  the  lens.  And  what  has 
here  been  stated  in  regard  to  a  flat  figure  holds  also  for 


86  OPTICS. 

any  material  object  the  parts  of  which  do  not  project 
too  far  beyond  a  plane  perpendicular  to  the  chief  axis. 
As  long  as  the  object  is  situated  at  a  greater 
distance  from  the  lens  than  the  focal  distance,  an 
actual  reunion  of  the  rays  of  light  occurs  upon  the 
other  side  in  the  image  plane;  and  thus  an  actual  or 
real  image  is  formed,  which  may  be  received  upon  a 
screen  and  thus  made  objectively  apparent.  The  real 
images  are  of  course  always  inverted  in  relation  to  the 
object. 

It  is  easy  to  show  this  relation  by  experiment. 
Let  a  lighted  candle  be  placed  in  front  of  a  lens  (fig. 
65),  and  somewhat  beyond  its  focal  distance,  by  a  little 


FIG.  (id. 


Heal  image  seen  through  a  convex  lens. 

shifting  to  and  fro  of  the  screen,  the  place  of  the  image 
may  be  easily  determined,  and  it  will  be  found  that  it  is 
situated  a  little  beyond  twice  the  focal  distance,  and  that 
it  is  inverted  and  enlarged.  If  the  position  of  the  screen 
and  candle  be  so  altered  that  the  candle  is  situated  a 
little  beyond,  and  the  screen  a  little  nearer  than  twice 
the  focal  distance  of  the  lens,  an  inverted  diminished  image 
of  the  flame  is  obtained  upon  the  screen.  Fig.  64 
exhibits  the  course  of  the  rays  in  both  cases  ;  if  a  b  be 
the  object,  A  B  is  its  real  image,  and  vice  versa. 

43.  If  an  object  be  situated  at  somewhat  less  than 


LENSES.  87 

the  focal  distance  from  the  lens,  no  real  image  of  it  can 
be  projected  by  the  lens.  For  the  rays  which  emanate 
from  one  of  its  points  (A,  fig.  66)  will  now  no  longer 
be  collected  into  one  point  on  the  other  side,  but  issue 


Virtual  image  with  a  convex  lens. 

divergingly  from  the  lens,  just  as  if  they  came  from 
a  point  a  situated  on  the  same  side  of  the  lens  but 
more  distant  from  it  than  the  point  A.  An  ob- 
server looking  through  the  lens  from  the  other  side 
sees  therefore  instead  of  the  small  object  A  B,  the 
enlarged  virtual  image  a  b,  which  is  erect  in  regard  to 
the  object.  On  account  of  this  well-known  action, 
convex  lenses  are  called  magnifiers.  Every  lens  specially 
destined  for  this  object  of  enabling  us  to  see  the 
enlarged  virtual  images  of  small  objects  is  called  a 
magnifying  glabs  (Lupe). 

44.  A  concave  lens  acts  at  each  part  like  an  acute- 
angled  prism,  the  refracting  angle  of  which  is  turned 
towards  the  principal  axis,  and  is  greater  the  further  the 
point  is  from  the  axis.  Every  ray  that  strikes  such  a 
lens  will  therefore  be  turned  away  from  the  axis,  and 
to  a  greater  extent  in  proportion  as  the  part  of  the 
lens  on  which  it  falls  is  further  from  the  axis.  Hence 
the  solar  rays,  which  are  directed  upon  this  biconcave 
lens  (fig.  67),  parallel  to  its  axis,  issue  divergingly  from 
the  other  side  of  the  lens  in  such  a  manner  that 


88  OPTICS. 

they  appear  to  proceed  from  a  point  F,  situated 
upon  the  axis  on  this  side,  which  we  may  designate  as 
the  apparent  or  virtual  focus.  Every  concave  lens  has, 
on  every  axis,  two  such  focal  points,  which  are  situated 
at  an  equal  distance  from  the  lens  on  either  side,  and 
have  the  same  significance  as  the  real  foci  of  a  convex 
lens.  The  virtual  focal  distance  is  proportional  to  the 
deflection  froui  the  axis  which  the  rays  of  light  ex- 
perience at  each  point  of  the  concave  lens. 

In  order  to  elucidate  the  action  of  concave  lenses, 
a  precisely  similar  series  of  observations  to  those 
already  given  in  the  case  of  convex  lenses  should  here 
be  inserted ;  but  to  avoid  repetition  it  will  be  sufficient 
if  the  more  important  cases  are  here  mentioned. 

A  cone  of  rays,  produced  by  a  convex  lens,  is  allowed 
to  fall  upon  a  concave  lens  (fig.  67)  in  such  a  manner 
that  the  rays  converge  towards  its  focal  point  F  on  the 
opposite  side ;  in  this  case  there  proceeds  from  the  other 
side  of  the  lens  a  cylinder  of  rays  parallel  to  its  chief 
axis.  If  the  incident  rays  converge  to  a  point  which  is 
more  distant  on  that  side  than  the  focus  of  the  lens, 

they  must  emerge  diverg- 
ingly :  but  if  they  converge 
— •  to  a  point  J5,  situated  nearer 
to  the  lens  (fig.  68),  they 
must  converge  after  refraction 
less  strongly  to  the  more  re- 

Virtual  focus  of  a  concave  lens.  . 

mote  point  A.     Kays,  lastly, 

which  are  emitted  divergingly  from  a  point  A,  as,  for 
example,  from  an  electric  lamp  placed  at  this  spot,  are 
rendered  still  more  divergent  by  the  lens,  as  if  they 
proceeded  from  a  point  B  situated  nearer  to  the  lens 
on  th  >  same  side. 


LENSES. 


89 


Hence  it  follows  that  a  concave  lens  can  form  a 
virtual  image  only  of  an  object,  whatever  may  be  the 
distance  that  this  is  from  it,  because  it  makes  the  di- 


FlG.  68. 


Action  of  a  concave  lens  on  convergent  and  divergent  raj  s. 

verging  rays  emitted  from  every  point  of  the  object 
still  more  divergent.  The  eye  of  an  observer  looking 
through  the  lens  (fig.  09)  receives  the  rays  emitted 
from  the  object  A  B  as  if  they  came  from  a  diminished 
erect  virtual  image  a  b.  On  account  of  this  diminishing 
action,  concave  glasses  are  called  diminishing  glasses, 
and  thus  we  see,  that  whilst  con  vex  lenses  are  analogous 


FlU.  G9. 


Virtual  image  formed  by  a  concave  lens. 

to  concave  mirrors  in  their  action,  concave  lenses  cor- 
respond to  convex  mirrors. 

45.  Of  the  various  forms  of  lenses  enumerated  in 
§  37  we  need  only  consider  the  biconvex  and  biconcave 
more  closely,  because  the  remaining  forms  entirely 
agree  in  their  action  with  these  representatives  of  these 
groups. 

The  lenses  of  the  first  group  possess  real  foci ;  they 
make  parallel  incident  rays  convergent,  and  unite  them 


90  OPTICS. 

into  one  point ;  the}'  make  convergent  rays  still  more 
convergent,  divergent  rays  less  divergent,  or  even  con- 
vergent. 

The  lenses  of  the  second  group  have  virtual  foci ; 
they  make  parallel  rays  divergent,  divergent  still  more 
divergent,  convergent  less  convergent,  or  even  di- 
vergent. 

Every  lens  which  becomes  thicker  towards  its  peri- 
phery has  virtual  foci ;  and  vice  versa,  for  the  focus  of  a 
lens  to  be  real  the  lens  must  be  thicker  in  the  middle 
than  at  the  edge. 

For  all  lenses,  however,  to  whatever  group  they  may 
belong,  the  general  statement  holds  good  that  rays, 
which  before  they  strike  upon  the  lens  pass  through  a 
single  point,  pass  also,  after  refraction,  through  a  single 
point  which  is  conjugate  to  the  first,  upon  the  axis 
passing  through  it. 


APPENDIX   TO   CHAPTER   VI. 

To  §  38.      The  angle  which  the  anterior  surface  of  a  lens 
fig.  70)  makes  at   the  point  Ii,  which  is  distant  K  P  =  k  from 


FIG.  70. 


Determination  of  the  focal  distance. 


the  axis,  with  the  posterior  surface  of  the  lens  at  the  opposite  point 
K',  or  in  other  words  the  refracting  angle  corresponding  to  the 
point  K,  is  equal  to  the  angle  C  K  L,  which  the  radii  C  TTand  C' K' 


LENSES.  91 

prolonged  to  A' from  th*1  centres  of  curvature  C  and  C'  form  with 
each  other,  because  these  radii  are  obviously  perpendicular  at 
K  and  K'  to  the  surfaces.  The  angle  C  K  L,  however,  as  external 
angle  of  the  triangle  CK  C",  is  equal  to  y  +  y1.  Presupposing 
that  the  lens  is  one  of  small  aperture,  the  angles  above  named,  as 
well  as  those  more  distant,  are  collectively  very  small,  and  in 
order  to  express  them  we  may  use  the  method  applied  above. 
(See  Appendix  to  Chapter  IV.) 

Consequently 

/J  i      §  A' 

y  =  -     „  and  y   =    -- — . 

If,  as  always  occurs  in  ordinary  cases,  the  thickness  of  the  lens 
is  very  inconsiderable  as  compared  with  its  radius  of  curvature, 
we  may,  without  risk  of  material  error,  take  C'  K'  instead  of  C'  K. 
If  therefore  we  indicate  the  radii  C  AT  and  C'  K'  respectively,  by  y 
and  r'  we  obtain 

7  ~~  T7  ~~  r1' 

The  refracting  angle  y  +  y'  at  the  point  K  is  therefore 

that  is  to  say,  it  is  proportional  to  distance  k  from  the  axis. 

We  now  know  (see  Appendix  to  Chapter  V.)  that  the  deflec- 
tion produced  by  an  acute-angled  prism  is  equal  to  (n  —  1) 
times  its  refracting  angle.  Every  ray  falling  upon  the  lens  at 
the  point  K  undergoes  therefore  the  deflection 


The  ray  S  K,  for  instance,  which  runs  parallel  to  the  axis, 
since  it  is  deflected  to  the  focal  point  F,  undergoes  a  deflection 
that  is  represented  by  the  angle  0,  which  the  refracted  ray  forma 
with  the  axis.  From  what  has  just  been  stated, 


92  OPTICS. 

The  angle  ^>  may  also  be  expressed  by 


F  K,  however,  if  the  small  thickness  of  the  lens  be  neglected, 
may  be  replaced  by  F  M,  that  is  to  say,  by  the  focal  distance  / 
of  the  lens,  so  that  we  get 


If  this  value  be  substituted  for  <f>  in  the  above  equation,  the 
factor  k,  common  to  both  sides,  may  be  eliminated,  and  we 
obtain  for  the  calculation  of  the  focal  distance  the  equation, 


/ 

The  very  fact  that  k  is  eliminated  from  the  equation  demon- 
strates that  all  rays  parallel  to  the  axis,  at  whatever  distance  k 
Irom  the  axis  they  may  fall  upon  the  lens,  unite  on  the  other 
side  in  the  single  point  F. 

It  appears,  further,  from  the  circumstance  that  the  radii  r 
and  r'  can  be  substituted  for  each  other  without  altering  the 
expression  for  the  focal  distance,  that  the  focal  distance  is  equal 
for  the  two  sides  of  the  lens. 

The  formula  shows  also  in  what  way  the  focal  distance  is 
dependent  upon  the  index  of  refraction  n  of  the  substance  of 
which  the  lens  is  composed.  For  a  biconvex  lens  composed  of 
crown  glass  (n  =  1'530),  for  example,  the  two  radii  of  curvature 
of  which  are  equal,  r1  =  r,  we  find 

7  r  r    ' 

consequently 


With  a  biconvex  lens  of  crown  glass  of  equal  curvature  on  both 
sides,  the  focal  distance  is  consequently  nearly  equal  to  the 
^adius  of  curvature,  that  is  to  say,  the  focus  is  very  nearly  co- 
incident with  the  centre  of  curvature.  For  a  similar  lens  com- 


LENSES. 


93 


posed  of  flint  glass  (n  =  1'635),  it  results  on  the  other  hand 
that 

/=  0-787.  r, 

and  for  a  lens  composed  of  Diamond 

(n  =  2-487) 
/only  =  0-336  .  r. 

From  this  it  is  evident  that  for  lenses  of  similar  form,  but  made 
of  different  materials,  the  focal  distance  becomes  smaller  as  the 
index  of  refraction  of  the  substance  used  increases. 

To  §  39.  In  order  to  determine  the  position  of  the  conju- 
gated points,  it  is  only  necessary  to  follow  any  given  ray  in  its 
course.  For  this  purpose  we  select  a  ray,  R  A  (fig.  71),  striking 
the  border  of  the'  lens,  which  is  refracted  in  the  line  A  S,  so  that 

FIG.  71. 


Determination  of  conjugate  points. 

R  and  S  are  conjugate  points.  /The  deflection,  y,  which  this  rny 
undergoes  at  A  is  the  same  in  amount  as  the  deflection  0  which 
the  ray  N  A  parallel  to  the  axis  experiences  at  the  same  point; 
that  is  to  say,  y  =  (ft.)  But  if  the  angles  which  the  rays  R  A 
and  A  S  make  with  tne  axis  be  indicated  by  a  and  /3,  y  =>  ^  +  &. 
It  results  consequently  that 


a  = 


If  the  distance  of  the  point  ^  from  the  lens  be  indicated  by 
a,  that  of  the  point  S  by  5,  the  focal  distance  by  /,  and  lastly, 
the  distance  of  the  point  A  from  the  axis  by  Jc,  the  equations 


94  OPTICS. 

are  obtained,  and  since  also 

k       k  _  k 
a       ~b~~f 

from  which  equation  the  magnitude  of  k  which  refers  to  the 
several  points  of  incidence  may  be  eliminated,  there  is  obtained 
for  the  determination  of  the  conjugate  points  the  equation 

n.  1  +  1=4. 

a       b       f 

which,  in  its  form  is  exactly  the  same  as  that  formerly  (see 
Appendix  to  Chapter  IV.)  found  for  the  spherical  mirror,  and 
expresses  distinctly  the  analogy  which  exists  between  mirrors 
and  these  lenses. 

The  equations  T.  and  II.,  which  are  primarily  deduced  for 
biconvex  lenses,  hold  nevertheless  for  every  form  of  lens,  if  we 
admit  the  curvature  for  a  plane  surface  to  be  indefinitely  great 
(=  oo  ),  for  a  concave  surface  negative  and  for  a  convex  surface 
positive.  And  according  as  in  the  Formula  I.,  the  value  of/  ig 
positive  or  negative,  the  lens  possesses  real  or  virtual  focal  points. 


OPTICAL  INSTRUMENTS. 


95 


CHAPTER  VII. 

OPTICAL    INSTRUMENTS. 

46.  REFERENCE  will  here  only  be  made  to  a  few  of 
the  numerous  applications  of  lenses  to  the  construction 
of  optical  instruments. 

For  experiments  in  optics  intended  to  be  rendered 
visible  to  many  persons,  the  light  of  the  sun,  on  account 
of  its  great  brilliancy,  is  employed  by  preference  ;  un- 

PIG.  72. 


Dubosq's  lamp. 

fortunately,  however,  in  the  cloudy  northern  heavens  it 
is  too  frequently   unavailable,  and  therefore,  in  order 

to  be  independent  of  the  variations  of   weather   and 

8 


96  OPTICS. 

of  daylight,  it  is  customary  to  substitute  for  the 
light  of  the  sun  that  of  an  intense  artificial  light,  as 
for  example,  that  of  the  electric  lamp. 

An  important,  and  for  many  experiments,  con- 
venient peculiarity  of  the  rays  of  the  sun  is  that  they 
are  nearly  parallel.  The  rays  of  the  electric  lamp,  on 
the  other  hand,  issue  divergingly  from  the  white-hot 
charcoal  points,  and  hence  if  they  are  to  be  used 
instead  of  the  sun's  rays  they  must  be  rendered 
parallel. 

This  is  effected  by  means  of  Dubosq's  lamp  (fig. 
72)  which  consists  of  a  square  box  supported  on  four 
brass  feet,  into  which  the  carbon-light  regulator  (or 
the  lime  light,  or  any  other  source  of  light)  is  intro- 
duced. 

The  light-point  is  so  placed  as  to  be  in  the  focus  of  a 
convex  lens  which  is  fixed  in  a  moveable  frame  at  the 
fore-part  of  the  box.  By  means  of  the  regulating  me- 
chanism the  carbon  points  can  be  made  to  occupy  this 
position  permanently.  The  rays  that  fall  upon  the  lens 
consequently  leave  the  lamp  parallel  to  each  other.  At 
the  back  of  the  box  is  a  concave  mirror,  the  object  of 
which  is  to  render  the  rays  proceeding  in  this  direction 
serviceable.  For  since  its  centre  of  curvature  is  coin- 
cident with  the  carbon  points,  it  returns  the  rays  to 
their  point  of  origin,  from  whence  they  pass  to  the  lens, 
and  having  been  rendered  parallel  by  this,  combine 
with  the  rays  emanating  from  the  points  which  are 
passing  directly  forwards. 

The  flame  can  be  so  used  as  to  produce  a  greatly 
magnified  image  of  the  form  of  the  carbon  points,  and 
the  play  of  the  arc  of  flame ;  for  if  the  lens  be  drawn  a 
little  way  out  of  the  tube  so  that  the  distance  of  the 


OPTICAL  INSTRUMENTS.  97 

charcoal  points  is  somewhat  greater  than  its  focal  dis- 
tance, an  inverted  and  enlarged  image  of  them  (fig. 
72 )  is  thrown  upon  the  opposite  screen.  We  see  between 
the  white-hot  carbon  points  the  far  less  brilliantly  lumi- 
nous violet  arc  of  flame  in  flickering  movement.  From 
time  to  time  white-hot  particles  are  detached  from  the 
blunt  and  excavated  positive  carbon  point,  and  fly  across 
to  the  negative  point,  which  remains  sharp ;  small 
globules  are  seen  moving  hither  and  thither  on  the 
surface  of  the  carbon,  as  though  they  were  in  a  state  of 
ebullition.  These  are  particles  of  molten  silex  which 
are  unfortunately  present  even  in  the  best  carbon  points, 
and  by  their  restless  movements  occasion  the  flickering 
of  the  luminous  arc,  whilst,  if  they  happen  to  occupy 
the  hottest  part  of  the  carbon  points,  they  cause  an 
immediate  diminution  in  the  intensity  of  the  flame. 

47.  The  experiment  just  described  is  identical  in 
principle  with  the  action  of  the  magic  lantern  (fig.  73). 
It  is  dependent  on  the  property  that  convex  lenses 
possess  of  forming  outside  of  or  beyond  twice  their 
focal  distance  a'n  inverted  and  enlarged  image  of  any 
object  situated  on  the  opposite  side  between  their 
focal  distance  and  twice  their  focal  distance. 

Pictures  or  photographs  serve  as  objects,  and  they 
are  placed  in  a  slit  in  front,  a  b,  and  are  strongly 
illuminated  by  the  light  of  the  lamp  L,  placed  within 
the  box,  which  is  intensified  by  the  lens  m  m  and  the 
concave  mirror  H  H.  In  front  of  the  slit  is  a  lens 
or  a  combination  of  two  lenses,  which  act  like  one 
of  short  focal  distance,  and  can  be  moved  by  means 
of  a  sliding  tube.  These  throw  an  enlarged  image 
of  the  object  upon  the  screen.  The  magic  lantern 
has  proved  of  great  service  in  illustrating  scientific 


98  OPTICS. 

lectures,  in  addition  to  the  amusement  it  affords  by 
its  phantasmagoric  representations,  dissolving  views, 
chromatropes,  &c. 

FIG.  73 


11 


Magic  Lantern. 


48.  The  sim  or  solar  microscope  (fig.  74)  is  founded 
upon  the  same  principle,  though  it  is  devoted  to 
thoroughly  scientific  objects.  Its  most  essential  part 
is  a  convex  lens  of  short  focus,  placed  in  a  small  tube  L, 
and  throwing  a  greatly  enlarged  image  upon  a  screen 
of  any  small  firmly-fixed  object,  usually  between  two 
glass  plates,  and  placed  somewhat  beyond  the  focus  of 
the  lens  L.  But  since  the  amount  of  light  proceeding 
from  the  small  object  is  diffused  over  the  relatively- 
enormous  surface  of  the  image,  it  is  easy  to  understand 
that  the  object  must  be  very  brilliantly  illuminated  if 
the  image  is  not  to  be  too  faint. 

The  strong  illumination  of  the  object  is  effected  by 
means  of  a  large  convex  lens  placed  at  the  extremity 
of  the  wide  tube  constituting  the  body  of  the  inst.ru- 


OPTICAL  INSTRUMENTS.  99 

inent;  this   unites  the   rays  of  light  required  for  the 
illumination  into  its  focus. 

By  means  of  the  screw  C  the  object  can  be  placed 
in  this  focus,  whilst  the  screw  D  serves  to  move  the 
lens  L  until  the  image  is  thrown  with  precision  on  the 
screen.  For  the  purpose  of  illumination  either  the 
light  of  the  sun  may  be  employed,  in  which  case  the 

FIG.  74. 


lilt; 

Solar  Microscope. 

apparatus  constitutes,  as  in  our  figure,  a  true  'solar 
microscope,'  which  can  be  placed  in  the  aperture  of  the 
Heliostat,  or  the  apparatus  may  be  attached  to  the 
frame  of  a  Dubosq's  lamp,  and  the  illuminating  power 
obtained  from  the  lime  or  electric  light,  in  which  case 
the  superfluous  names  of  '  photo-electric  microscope ' 
and  '  oxy- hydrogen  microscope '  have  been  applied 
to  it. 

The  solar  microscope  proves  of  great  service  for  the 
objective  representation  of  small  objects  in  scientific 
lectures.  During  the  siege  of  Paris  such  a  microscope, 
illuminated  by  the  electric  light,  was  made  use  of  in 
order  to  project  upon  a  screen  and  render  available  for 


J  00  OPTICS. 

several  copyists  images  of  the  tiny    photographic  de- 
spatches that  were  brought  by  the  carrier  pigeons. 

49.  If  a  convex  lens  be  fitted  into  the  opening  of  a 
shutter  of  a  darkened  chamber,  a  variegated  picture 
appears  upon  the  opposite  screen,  like  those  which  we 
formerly  (§  13)  obtained  from  a  small  opening  with- 
out a  lens,  but  of  greater  clearness  and  sharpness. 
For  the  lens  projects  real  inverted  images  of  external 
objects  situated  at  more  than  double  its  focal  distance 
upon  a  screen  which  lies  between  its  single  and  double 
focal  distance.  But  inasmuch  as  the  external  objects 
are  situated  at  very  variable  distances,  it  cannot  be  ex- 
pected that  the  images  of  all  should  appear  with  equal 
sharpness  of  outline  upon  the  screen.  In  fact  the 
screen  can  easily  be  arranged  in  such  a  manner  that 
the  image  of  a  distant  tower  is  projected  with  sharp 
outlines ;  but  then  the  leaves  of  a  tree  near  at  hand 
appear  indistinct  and  confused.  In  order  to  obtain  a 
distinct  image  of  the  tree  the  screen  must  be  removed 
to  a  somewhat  greater  distance,  but  the  definition  of 
the  outline  of  the  tower  is  then  again  sacrificed. 

These  defects  in  the  definition  are  nevertheless  less 
considerable  than  might  at  first  sight  appear.  It 
need  on}y  be  called  to  mind  that  if  an  object  is  removed 
from  twice  the  focal  distance  from  the  lens  to  infinity, 
its  image  moves  over  merely  the  short  distance  that  inter- 
venes between  the  double  and  the  single  focal  distance ; 
a  great  difference  in  the  distance  of  the  object  thus  cor- 
responds to  only  a  small  shifting  of  the  image-plane, 
and  indeed  this  is  smaller  in  proportion  to  the  remote- 
ness from  the  lens  of  the  nearest  object  the  image  of 
which  is  cast  upon  the  screen.  It  follows  that  all 
objects  lying  beyond  certain  limits  are  depicted  with 


OPTICAL  INSTRUMENTS.  101 

tolerably  satisfactory  sharpness  of  definition   upon   a 
plane  situated  near  the  focal  point. 

The  dark  chamber  the  object  of  which  is  to  keep 
out  collateral  light  from  the  image,  may  be  replaced 
by  a  box  the  interior  of  which  has  been  blackened 
(fig-  75)- 

FIG.  75. 


Camera  obscura. 

The  lens  is  fitted  into  a  metal  tube  i  which  can  be 
made  to  slide  in  the  draw  tube  h  by  means  of  a  screw 
the  head  of  which  is  shown  at  r.  The  box  a  is  open 
at  the  back  and  receives  a  second  box  6,  open  in  front ; 
in  this  is  a  plate  of  ground  glass,  the  place  of  which 
can  be  shifted  by  pushing  in  or  out  the  box  6,  and  which 
receives  the  image. 

The  nearer  the  object  the  ima.ge  of  which  is  cast 
upon  the  ground-glass  screen  is,  the  further  must  the 
box  ~b  be  withdrawn  from  the  box  a.  The  fine  adjust- 
ment is  effected  by  the  movement  of  the  lens  by  means 
of  the  screw  r. 

This  apparatus,  which  in  its  now  portable  form  has 
received  the  name  of  camera  obscura.,  remained  a 
mere  plaything  from  the  time  of  its  discovery  by  Porta 
in  the  sixteenth  century  until  recently,  when  its  fleeting 
images  have  been  successfully  fixed  by  photography. 


102 


OPTICS. 


It  has  now,  however,  risen  to  be  the  chief  implement  of 
this  highly  developed  branch  of  art. 

The  human  eye  is  only  a  small  camera  obscura  of 
wonderfully  perfect  construction.  The  crystalline  lens, 
in  common  with  the  transparent  refracting  media  filling 
the  globe,  casts  upon  the  retina  lining  its  interior  an 
inverted  real  image  of  the  external  world,  the  impres- 
sion of  which  is  conveyed  to  our  minds  by  the  functional 
activity  of  the  optic  nerves.  The  physiological  and 
psychological  processes  by  means  of  which,  in  addition  to 
the  physical,  vision  is  effected,  do  not  belong  to  the 
domain  of  physical  optics.  Their  consideration,  as  well 
as  the  physiology  of  the  organs  of  vision,  must  be  passed 
over. 

50.  The  system  of  lenses  we  have  here  described 
projects  real  images,  which  when  received  upon  a 
screen  become  apparent  to  many 
observers  simultaneously.  We  shall 
now  refer  to  a  series  of  optical 
instruments  the  virtual  images  of 
which  are  only  visible  to  a  single 
observer. 

Every  instrument  by  means  of 
which  enlarged  images  of  small  and 
near  objects  are  seen,  is  called  a 
'microscope.'  In  this  sense  the 
lens  above  mentioned  (p.  87)  must 
be  regarded  as  a  (  simple  micro- 
scope.'  The  compound  microscope 
1  s  possesses  a  far  greater  sphrre  of 

Action  of  the  Microscope. 

usefulness.     It  consists  essentially 

of  two  convex  lenses  (fig.  76),  which  are  placed  upon  a 
common  axis  (at  a  distance  of  somewhat  more  than  the 


FIG.  77. 


OPTICAL,  INSTRUMENTS.  103 

sum  of  tlieir  focal  distances./  One  of  these  lenses  (a  b) 
of  very  short  focus  is  applied  to  the  object,  and  is  there- 
fore termed  the  objective.  It  projects  to  8  R  an  inverted 
and  enlarged  real  image  of  any  small  object  (rs),  placed 
at  a  somewhat  greater  distance  than  its  focus,  which 
acts  as  a  luminous  object  to  the  glass  nearest  the  eye, 
or  ocular.  This  image  is  seen  as  the  virtual  image 
S'  R',  still  further  enlarged  by  means  of  the  ocular, 
from  which  it  is  somewhat  less  distant  than  the  focal 
distance  of  the  lens. 

Fig.  77  exhibits  the  form  and  arrangement  of  the 
ordinary  microscope.  The  ocular  n,  and  the  objective 
o,  are  placed  in  a  vertical  tube,  which, 
owing  to  its  being  accurately  fitted 
into  a  brass  sheath,  n,  is  moveable 
with  slight  friction. 

The  fine  adjustment  is  effected  by 
turning  the  head  of  the  screw,  k. 
The  object,  which  is  usually  trans- 
parent and  fixed  upon  a  glass  slide, 
is  placed  upon  the  stage,  p  p,  and 
illuminated  by  light  reflected  from 
below  by  the  mirror,  s. 

If  the  tube  of  the  microscope  be 
drawn  out  so  far  that  the  i  mage  S  R  is 
formed  outside  of  or  beyond  the  focal 
distance  of  the  ocular  lens,  this  lens 
projects  a  real  image  of  the  image 
S  R,  which  can  be  received  upon  a 
screen.  In  order,  however,  that  this  enlarged  image 
should  be  sufficiently  luminous,  the  small  object  must 
be  very  strongly  illuminated  by  the  light  of  the  sun,  or 
by  that  of  the  lime  light  or  electric  lamp.  The  light 


Microscope. 


104 


OPTICS. 


FIG.  7 


intended  for  illumination  must  therefore  be  concentrated 
upon  the  object  a  by  means  of  a  large  convex  lens,  I 

(fig.  78),  aided  by  the  mir- 
ror s.  The  real  image  of 
the  image  6,  which,  on  ac- 
count of  the  vertical  posi- 
tion of  the  microscope  tube, 
must  be  formed  on  the 
ceiling  above,  is  thrown  to 
the  side  towards  c  upon  a 
paper  screen  by  means  of 
the  prism  p  set  at  the  angle 
of  total  reflexion.  This 
arrangement  enables  us  to 
make  use  of  any  ordinary 
microscope  as  a  solar 
microscope. 

51.  The  essential  fea- 
tures of  Kepler's,  or  the 
astronomical  telescope, 
(fig.  79)  are  that  two  convex 
lenses,  nameljr,an  objective, 
o  o,of  longer,  and  an  ocular, 
v  v,  of  shorter  focus,  are 
placed  on  an  axis  common  to  both  at  about  the  dis-  ( 
tance  from  each  other  of  the  sum  of  their  focal  dis- 
tances. The  objective  forms  near  its  focus  an  inverted 
real  image,  b  a,  of  a  remote  object,  A  B,  which  is 
seen  through  the  ocular,  as  through  an  ordinary  lens, 
in  the  form  of  an  enlarged  virtual  image,  b'  a'.  The 
visual  angle  V  m  a' ',  under  which  this  image  is  per- 
ceived, is  larger  than  the  visual  angle,  A  C  B,  under 
which  the  object  would  be  seen  by  the  naked  eye,  which 


Mode  )f  showing  the  image  of  a 
microscope  as  an  object. 


OPTICAL  INSTRUMENTS. 


105 


explains  the  magnifying,  or,  if  we  may 
so  call  it,  approximating  action  of  the 
instrument.  As  regards  the  further 
arrangement  of  Kepler's  telescope,  the 
objective  is  placed  at  the  anterior  ex- 
tremity, k,  of  a  tube  of  appropriate 
length  (fig.  80),  which  at  the  back  part 
is  provided  with  a  narrower  piece,  in 
which  the  tube,  t,  containing  the  ocular, 
o,  can  be  moved  to  effect  perfect  defini- 
tion by  means  of  a  screw.  Yery  large 
instruments  of  the  same  kind  employed 
for  astronomical  observations  are  called 
refractors. 

Kepler's  telescope  is  rendered  much 
more  serviceable,  not  only  for  astrono- 
mical purposes  but  also  for  physicists  and 
engineers,  by  means  of  the  cross  threads. 
These  consist  of  two  fine  threads  of  a 
spider's  web,  which  are  arranged  at  right 
angles  to  each  other,  decussating^  ex- 
actly in  the  axis  of  the  telescope,  and 
are  placed  at  the  point  where  the  image, 
b  a  (fig.  79)  is  formed,  in  consequence 
of  which  they  must  necessarily  be  seen 
distinctly  with  the  ocular.  If  the  image 
of  a  remote  object,  as,  for  example,  that 
of  a  fixed  star,  appears  at  the  point  of 
decussation  of  the  threads,  the  axis  of 
the  telescope  is  directed  straight  to  this 
point,  and  its  position  gives  the  direc- 
tion of  the  visual  line  from  the  eye 
to  the  star.  Kepler's  telescope  is 


^TBR 

OF  THE. 


106 


OPTICS. 


therefore  employed  in  all  our  instruments  for  measuring 
angles. 

In  the  determination  of  the  index  of  refraction  (§  35), 
it  enables  us  to  measure  the  slightest  deflection  effected 
by  a  prism.  An  instrument  termed  a  theodolite  is  made 


FIG.  80. 


FIG.  81. 


Astronomical  telescope. 

use  of  for  the  same  purpose  (fig.  81)  ;  it  consists  of  a 
horizontal  disk  capable  of  rotation  around  its  centre 
(the  indicator  disk),  and  a  telescope  supported  upon 
trunnions.  Two  markers  exactly  opposite  each  other 
(Nonia)  of  the  revolving  disk  point 
to  an  immoveable  circle  (limbus)  sur- 
rounding it,  which  is  divided  at  its 
circumference  into  degrees.  In  order 
to  determine  the  deflection  of  a  prism, 
the  telescope  is  first  directed  to  a  nar- 
row and  remote  source  of  light ;  as, 
for  example,  a  vertical  slit  in  the 
shutter,  until  the  image  of  the  slit 
coincides  with  the  vertical  thread  of 
the  cross  threads,  and  the  nonia 
are  read  off.  The  telescope  with  the 
indicator  circle  is  then  turned  till 
the  slit  is  again  perceived  to  coincide  exactly  with 
the  cross  threads  through  the  prism  placed  in  front  of 
the  objective,  and  'the  nonia  are  again  read  off".  The 
difference  between  the  two  readings  gives  the  angle  of 
deflection,  b  m  c,  sought  for. 


Instrument  for  measuring 
the  prismatic  deflection. 


OPTICAL   INSTRUMENTS.  107 

In  the  mirror  sextant  also  (fg.  24),  a  Kepler's 
telescope  is  usual  for  exact  vision. 

If  the  tube  containing-  the  ocular  of  a  Kjepler's 
telescope  be  moved  so  that  the  image,  b  a  (fig/jpa),  is 
more  distant  from  the  eye-piece  than  its  focal  distance, 
a  real  but  inverted  (and  therefore  in  regard  to  the  object 
itself  erect)  image  of  the  image  b  a  is  projected.  In 
this  way  an  image  of  the  disk  of  the  sun  may  be 
thrown  upon  a  screen  one  metre  in  diameter,  in  which 
the  sun  spots  are  plainly  visible. 

52.  By  means  of  Kepler's  telescope  objects  are  seen 
inverted,  which  is  of  little  importance  in  astronomical 
observations,  but  is  objectionable  in  the  observation  of 
remote  objects  upon  the  surface  of  the  earth. 

This  inconvenience  is  overcome  by  replacing  the 
simple  ocular  acting  like  a  lens  by  a  feebly  magnifying 
compound  microscope,  which  again  inverts  the  inverted 
image.  The  compound  ocular  of  the  terrestrial  tele- 


FlG.  82. 


Terrestrial  telescope. 


scope  is  usually  composed  of  four  convex  lenses  fixed 
in  one  tube.  This  arrangement  is  seen  in  fig.  82, 
which  represents  a  portable  telescope  with  draw  tubes, 
or,  in  other  words,  one  that  is  capable  of  being  shut  up. 
53.  Objects  are  also  seen  erect  with  the  Galilean, 
or  Dutch  telescope.  In  this  form  of  the  instrument 
the  real  image,  I  a  (fig.  83)  of  the  object  A  B  thrown  by 
the  convex  objective,  o  o,  is  not  formed,  for  the  rays 
here,  converging  as  they  do  towards  every  image,  strike 


108 


OPTICS. 

the  concave  ocular,  v  v,  which  renders 
them  so  far  divergent  that  they  appear 
to  come  from  the  vertical  erect  image 
of  b'.  Fig.  83  shows  very  distinctly  the 
course  of  the  rays  of  light  proceeding 
from  the  point  A  of  the  object.  For  the 
image  a'  ~bf  to  be  seen  under  a  larger 
visual  angle  than  the  object  looked  at 
with  the  naked  eye,  the  virtual  focal 
distance  of  the  ocular  must  be  smaller 
than  the  real  focal  distance  of  the  objec- 
tive, and  the  two  lenses  are  accordingly 
placed  at  about  the  difference  of  these 
two  distances  from  each  other. 

The  usual  form  given  to  the  instru- 
ment is  shown  in  fig.  84.  As  no  real 
image  is  formed  by  the  objective,  no 
cross  wires  can  be  inserted  ;  Galileo's 
telescope  is  consequently  not  applicable 
as  a  measurer..  Nor  again  is  it  possible 
to  obtain  any  very  high  magnifying 
power  by  its  means.  On  the  other  hand, 

FIG.  84. 


Galileo's  telescope. 


on  account  of  its  small  length  it  is 
•  extremely  convenient  as  a  pocket  tele- 
',  scope,  and  is  appropriate  therefore  for 
J^  the  use  of  opera  glasses  (with  double  or 


OPTICAL   INSTRUMENTS.  109 

triple    magnifying  power),   and  to  the  so-called  field 
glasses,  which  are  able  to  magnify  20  or  30  diameters. 

54.  It  is  very  intelligible  that  on  account  of  the 
very  similar  behaviour  of  lenses  and  spherical  mirrors, 
telescopes  can  be  constructed  in  which  a  concave  mirror 
plays  the  part  of  the  objective.  Tig.  85  shows  the 
construction  of  a  Newtonian  telescope.  The  concave 
mirror,  S  S,  placed  at  the  bottom  of  a  correspondingly 


FIG.  85. 


Action  of  Newton's  reflecting  telescope. 

wide  tube,  open  in  front,  collects  the  rajs  of  light 
coming  from  a  remote  object  to  form  a  real  inverted 
image  at  a.  Before,  however,  the  union  is  effected 
they  are  thrown  to  one  side  by  a  plane  mirror,  p,  inclined 
at  an  angle  of  45°  to  the  axis  of  the  tube,  so  that  the 
image  is  thrown  to  6,  when  it  can  be  observed  in  the 
direction  o  b  through  the  convex  ocular  o,  as  through 
a  microscope. 

The  reflexion  of  the  small  image  to  the  side  is 
necessary,  because  if  the  little  image  a  be  looked  for 
from  the  front,  the  head  of  the  observer  would  obstruct 
the  passage  of  light  to  the  mirror.  In  the  colossal 
telescopes  (Reflectors)  of  Herschel  and  Lord  Rosse,  the 
mirrors  of  which  are  from  1  to  2  metres  in  diameter, 
the  use  of  such  a  second  mirror,  and  the  consequent 


110 


OPTICS. 


loss  of  light,  is  avoided  by  a  simple  artifice.  The  con- 
cave mirror  (fig.  86)  is  a  little  inclined  to  the  axis  of 
the  tube ;  consequently,  the  real  image,  a,  comes  to 
lie  close  to  the  circumference  of  the  tube,  and  can  be 


FIG.  86. 


FIG.  87. 


Action  of  the  reflecting  telescope  with  anterior  opening. 

observed  through  an  ocular,  o,  in  the  same.  The  head 
of  the  observer  is  evc}n  here,  no  doubt,  partly  in  front 
of  the  aperture  of  the  mirror,  but  on  account  of  the 
large  size  of  the  latter  it  is  of  little  importance.  Herschel 
called  his  instrument  '  a  front  view  telescope.' 

In  using  Newton's  reflecting  telescope  the  observer 
has  the  object  looked  at  to  his 
side  ;  in  a  front  view  telescope 
he  turns  his  back  upon  it.  This 
circumstance,  which  excludes 
direct  vision  for  searching  pur- 
poses, as  well  as  the  inversion  of 
the  image,  render  both  instru- 
ments inconvenient  for  the  ob- 
servation of  terrestrial  objects. 
In  Gregory's  reflecting  telescope, 
the  external  appearance  of  which 
is  shown  in  fig.  87,  these  evils 
are  avoided.  The  concave  mirror,  s  s  (fig.  88),  is  per- 
forated by  a  circular  opening  in  its  centre,  and  the 


Gregory's  reflecting  telescope. 


OPTICAL  INSTRUMENTS.  Ill 

ocular,  o,  is  placed  in  a  tube  behind  this  aperture.  The 
diminutive  inverted  real  image  of  a  remote  object  is 
formed  at  a,  somewhat  beyond  the  focal  distance  of  a 
small  concave  mirror,  F.  This  throws  to  b  a  once  more 
inverted,  and  consequently  in  relation  to  the  object, 
•arect  image,  which  may  be  looked  at  through  the  ocular 
as  with  a  lens.  The  fine  adjustment  is  effected  by 

FIG.  88. 


Action  of  Gregory  s  reflector. 

shifting  the  little  mirror,  F,  by  means  of  the  shaft,  m  n, 
which  is  provided  at  m  with  a  screw  and  at  n  with  a 
head  for  turning  it.  (  It  is  only  in  the  construction  of 
7  very  large  instruments  that  reflectors  offer  any  advan- 
tages over  refractors^/  The  use  of  the  smaller  reflecting 
telescopes  was  formerly  very  general,  when  the  mode 
of  production  of  objectives  in  the  perfection  desired  was 
not  understood  ;  they  give,  however,  only  faint  images, 
and  cannot  now  compete  with  refractors,  though  very 
recently  they  have  again  undergone  great  improve- 
ment by  the  application  of  silvered  glass  instead  of 
easily  oxidisable  fused  metal  mirrors. 


112  OPTICS. 


CHAPTER  VIII. 

DISPERSION    OF    COLOUR. 

55.  THE  inferior  (positive)  carbon  point  of  the  electric 
lamp  is  now  to  be  replaced  with  a  thick  cylinder  of  carbon 
excavated  on  its  free  surface  for  the  reception  of  sub- 
stances the  behaviour  of  which  in  the  arc  of  the  electric 
flame  is  desired  to  be  investigated.  After  placing  the  ap- 
paratus in  the  Dubosq's  lamp,  a  fragment  of  the  wax-like, 
silvery  metal  Sodium  is  inserted  into  the  carbon  cup,  and 
the  two  poles  are  approximated.  At  the  instant  of  their 

contact,   the    current  passes  through  the 
FIG.  80. 

carbon    electrodes    and  the   little   ball   of 

n:etal,  which  quickly  evaporates  and  fills 
the  arc  of  flame  with  its  vapour.  The 
whole  process  may  be  distinctly  followed 
upon  a  screen  on  which  an  enlarged  image 
of  the  carbon  pole  is  thrown  by  the  lens 
when  somewhat  drawn  out.  Owing  to 
the  metal  vapour  which  rises  from  the  in- 
ferior carbon  point,  the  flame  acquires  a 
higher  degree  of  conductivity.  The  poles 
can  therefore  be  removed  to  a  much 
greater  distance  from  each  other  without 
extinguishing  the  arc  of  light  which  now 
of  forms  a  long  flame,  shining  with  a  daz- 
'  zling  yellow  light  (fig.  89),  whilst  the  carbon 
points,  on  account  of  their  greater  distance  from  one 


DISPERSION   OF  COLOUR.  113 

another,  glow  much  less  brightly,  and  give  off  much  less 
light  than  was  the  case  in  the  experiments  (§  46) 
formerly  made  with  pure  carbon  points. 

This  yellow  light  of  the  vapour  of  Sodium  glowing 
in  the  electric  flame  may  now  be  used  for  other  experi- 
ments.    In  the  first  place  the  lens  of  the  Dubosq's  lamp 
may  again  be  pushed  to  a  sufficient  distance  inwards  to  ") 
allow  its  focus  to  be  situated  in  the  arc  of  light ;  its  ( 
rays  are  then  rendered  parallel. 

The  opening  from  which  a  broad  cylinder  of  rays 
now  emanates  is  closed  with  a  cap  having  a  small  ver- 
tical slit  in  it,  and  the  slender  beam  of  parallel  rays 
proceeding  from  the  slit  falls  upon  a  convex  lens."* 

If  the  lens  be  placed  in  a  proper  position,  it  throws  a 
well-defined  image  of  the  narrow  slit  upon  the  screen, 
which  of  course  exhibits  the  yellow  colour  of  the 
source  of  light  employed. 

A  prism  is  next  placed  in  the  erect  position  behind 
the  lens  in  such  a  manner  that  its  refracting  angle  is 
vertical,  and  is  consequently  parallel  to  the  slit.  The 
light  proceeding  from  the  lens  is  deflected  away  from 
the  refracting  angle  of  the  prism,  and  the  image  of  the 
slit  is  exhibited,  shifted  laterally  upon  the  screen,  but 
otherwise  unaltered,  appearing  as  a  slender  vertical 
yellow  streak.  (The  prism  as  in  all  cases  is  arranged 
so  as  to  give  its  minimum  refraction.)  Up  to  this 
point  the  experiment  teaches  nothing  new.  Every- 
thing takes  place  as  might  be  anticipated  from  our 
knowledge  of  the  action  of  lenses  and  prisms.  But 
if  the  electric  current  be  interrupted,  in  order  that  a 
new  and  clean  carbon  point  may  be  inserted  and  a  frag- 

*  The  lens  must  be  achromatic.     See  Chapter  IX. 


114  OPTICS. 

ment  of  Lithium  deposited  in  its  cavity,*  the  arc  of 
flame  assumes  a  splendid  red  tint,  as  does  also  the 
image  of  the  slit,  whether  thrown  directly  upon  the 
screen  or  displaced  by  the  prism.  We  observe,  however, 
that  the  deflected  image  is  now  less  distant  from  the 
position  of  the  direct  image  than  in  the  previous  ex- 
periment. The  red  light  of  Lithium  is  thus  seen  to  be  less 
strongly  refracted  through  the  same  prism  than  the  yellow 
light  of  Sodium. 

The  same  experiment  may  be  repeated,  taking  a 
fresh  piece  of  carbon  each  time,  with  the  metals  Thal- 
lium and  Indium.  The  splendid  green  light  of  Thallium 
is  more  strongly  refracted  than  the  yellow  light  of  Sodium, 
whilst  the  blue  light  of  Indium  undergoes  a  still  stronger 
refraction  than  that  of  Thallium. 

It  is  thus  seen  that  the  four  kinds  of  light  which 
have  been  compared,  besides  the  differences  of  colour 
they  present  to  the  eye,  differ  amongst  themselves  in 
the  circumstance  that  their  refrangibility  is  progres- 
sively greater  in  the  order,  red,  yellow,  green,  and  bine. 

A  mixture  of  the  four  metals,  Lithium,  Sodium, 
Thallium,  and  Indium  may  now  be  placed  upon  the 
lower  carbon  pole.  The  glowing  vapours  of  all  four 
metals  are  thus  present  at  the  same  time  in  the  flame. 
In  the  first  place,  let  the  direct  image  of  the  slit  which 
the  lens  throws  upon  the  screen  without  the  inter- 
vention of  the  prism  be  considered.  As  in  the  pre- 
vious experiment,  it  appears  as  a  bright  sharply-defined 
vertical  line,  in  which  nevertheless  it  is  impossible  to 
distinguish  any  definite  tint  of  colour.  The  impression 
received  might  rather  be  called  that  of '  white '  light. 

*  Instead  of  the  metal  itself,  one  of  its  salts,  as  forinstance  the  Lithium 
carbonate,  may  be  used. 


DISPERSION   OF   COLOUR. 


115 


On  placing  the  prism  again  behind  the  lens,  there  ap- 
pear upon  the  screen  no  longer  one  but  four  refracted 
images  of  the  slit.  We  see  the  four  coloured  bands, 
which  we  had  before  us  in  the  previous  experiment 


FIG.  90. 


Ditierent  deflection  of  different  coloured  rays  of  light. 

separately,  now  coincidently  one  beside  the  other,  each 
occupying  its  own  proper  place,*  and  each  being  ar- 
ranged in  order  according  to  its  specific  refrangibility 
(fig.  90). 

The  white  light  of  the  electric  flame  is  consequently 
compound,  or  is  a  mixture  of  four  different  kinds  of  light, 
which,  owing  to  their  different  refrangibility,  are  sepa- 
rated from  one  another  by  the  prism.  Neither  of  the 
kinds  of  light  composing  the  flame  undergo'vany  further 
decomposition  by  the  prism,  and  hence  they  are  termed 
simple  or  homogeneous  light.  The  prismatic  decomposi- 

*  It  is  obvious  that  the  prism  can  only  be  arranged  with  precision  for 
the  minimum  deflection  of  one  kind  of  light.  At  the  same  time  if  this  be 
the  case  for  one  kind  of  light,  as  for  instance  for  the  Sodium,  the  refrac- 
tion of  the  other  kinds  of  light  must  be  nearly  at  its  minimum. 


116  OPTICS. 

tion  of  compound  light  into  its  constituents,  by  reason 
of  their  different  refrangibility,  is  called  the  dispersion 
of  light. 

It  is  not  every  chemical  substance  which,  when 
brought  into  the  electric  flame,  gives  so  simple  a  light 
as  the  four  named  above.  If,  for  example,  Strontium, 
or  a  salt  of  this  metal,  be  placed  on  the  lower  carbon 
point,  the  a,rc  of  flame  assumes  a  brilliant  red  colour, 
which,  however,  is  not  homogeneous  like  that  of 
Lithium,*  since  by  breaking  it  up  with  the  prism  a 
group  of  red  and  orange- coloured  lines  may  be  ob- 
tained upon  the  screen,  and  lastly,  at  a  considerable 
distance  from  them,  a  beautiful  blue  line,  none  of  which, 
however,  coincide  with  the  lines  of  any  of  the  above- 
mentioned  metals,  for  the  brightest  red  band  is  some- 
what more  strongly  refracted  than  the  Lithium  band,  and 
the  blue  band  is  less  refracted  than  the  Indium  band. 

The  arc  of  flame  is  coloured  yellowish  green  by  a  salt 
of  Barium.  By  prismatic  dispersion,  a  group  of  orange- 
yellow  and  green  lines  are  obtained  of  which  again 
none  agrees  with  those  above  mentioned  in  its  refran- 
gibility.  A  characteristic  line  or  group  of  lines  thus 
corresponds  to  every  metallic  element,  and  serves  to 
indicate  its  presence  in  a  mixture  of  luminous  vapours. 

56.  The  same  method  of  decomposing  light  which 

*  The  light  of  Lithium  is,  however,  itself  not  completely  homogeneous, 
since  in  addition  to  the  red,  it  contains  an  orange-coloured  constituent 
which  is  refracted  more  strongly  than  the  red  of  the  Lithium  and  yet  less 
strongly  than  the  yellow  of  Sodium.  The  Indium  further  shows  besides  the 
blue  a  still  more  strongly  deflected  violet  stria.  The  orange- coloured  con- 
stituent of  the  Lithium  light  as  well  as  the  violet  of  the  Indium  light  being 
very  faint  as  compared  with  the  red  of  the  former  and  the  blue  of  the  latl  er, 
are  for  the  time  neglected  in  the  above  experiments.  The  yellow  light  of 
Sodium,  on  the  other  hand,  as  well  as  the  green  of  Thallium,  may  be  re- 
garded as  homogeneous  kinds  of  light. 


DISPERSION   OF   COLOUR.  117 

has  previously  been  made  use  of  in  examining  the  light 
of  the  electric  flame  saturated  with  metallic  vapours, 
may  now  be  applied  to  the  dazzling  light  of  the  glowing 
carbon  points  itself.  For  this  purpose  the  earlier  ar- 
rangement in  which  both  poles  consist  of  small  cylinders 
of  carbon  may  be  reverted  to.  The  flame  is  short  between 
their  approximated  extremities,  and  its  feeble  light  is 
far  surpassed  by  the  glow  of  the  white-hot  carbon 
points.  Before  the  prism  is  interposed,  the  lens  throws 
upon  the  screen  a  sharply-defined  white  image,  the  slit 
having  a  height  of  about  30  centimetres  (13  inches), 
and  very  small  breadth.  If  the  prism  be  now  placed 
behind  the  lens,  there  appears  deflected  laterally  upon 
the  screen  a  beautiful  coloured  band  which  stretches 
horizontally  to  the  length  of  nearly  a  metre,  but  which 
preserves  the  height  of  the  slit  in  the  vertical  direc- 
tion (about  80  centimetres).  The  band  shows  at  the 
end  which  lies  nearest  to  the  slit  a  beautiful  red,  then 
follow  in  order  the  colours  orange,  yellow,  green,  light 
blue,  indigo,  and  finally  violet.  No  one  of  the  colours 
is  sharply  defined  from  the  adjoining  ones,  but  each 
passes  into  the  next  through  all  possible  intermediate 
tints.  This  coloured  band  (indicated  in  fig.  90  by 
shadow  tinting),  is  called  the  Spectrum. 

The  experiments  made  above  with  the  electric  light 
point  out  how  the  formation  of  the  spectrum  may  be  ex- 
plained. Every  homogeneous  kind  of  light  contained  in  the 
beam  striking  the  prism  forms  on  the  screen  a  slender 
image  of  the  slit  exactly  at  the  spot  which  corresponds 
to  the  refrangibility  of  that  kind  of  light.  The  spec- 
trum which  extends  through  a  wide  region  of  refrangi- 
bility is  consequently  to  be  explained  as  the  uninter- 
rupted succession  of  innumerable  images  of  the  slit 


118  OPTICS. 

which  are  arranged  in  the  form  of  a  continuous  band. 
The  conclusion  is  thus  arrived  at  that  the  white  light 
of  the  electric  glowing  carbon  is  composed  of  innumei- 
able  homogeneous  kinds  of  light,  each  of  which  pos- 
sesses a  definite  refrangibility  in  regard  to  the  prism. 
The  refrangibility  continuously  increases  from  the  red 
which  is  the  least,  to  the  violet  which  is  the  most,  re- 
frangible light. 

That  the  colours  of  the  spectrum  are  really  homo- 
geneous may  be  proved  by  the  following  experiment.  The 
FIG  9J  spectrum  is  received  upon 

a  screen  in  which  is  a 
narrow  vertical  slit  (fig.  91). 
If  this  be  placed  in  the 
middle  of  the  green  this 
coloured  light  only  passes 
through  it,  and  it  undergoes 
no  further  decomposition 
if  it  be  made  to  pass  through 

of  the  spectrum.  -i          .  i  i     T_ 

a  second  prism  placed  be- 
hind the  slit.  Under  these  circumstances  it  is  merely 
deflected,  without  any  alteration  being  effected  in  its 
colour,  and  is  consequently  demonstrated  to  be  homo- 
geneous. The  same  holds  for  all  the  other  colours  of 
the  spectrum.  The  groups  of  lines  produced  by  the 
metallic  vapours  may  also  be  regarded  as  spectra  in 
which  only  a  limited  number  of  kinds  of  light  (or  even 
only  a  single  kind)  is  represented.  In  this  sense,  for 
example,  it  is  said  that  the  spectrum  of  Lithium  consists 
of  a  red  and  of  an  orange  red,  that  of  Thallium  only  of 
a  single  green  line.  In  opposition  to  this  interrupted 
spectrum,  that  of  the  carbon  points  is  called  an  uninter- 
rupted or  continuous  spectrum. 


DISPERSION   OF   COLOUR.  119 

In  giving  an  explanation  of  the  continuous  spectrum 
as  a  succession  of  closely-arranged  images  of  the  slit,  it  is 
requisite  to  explain  why  a  narrow  slit  parallel  to  the  re- 
fracting angle  of  the  prism  is  selected  as  the  opening  for 
the  incident  rays.     If  the  aperture  had  some  other  form, 
as  for  instance  a  circular  one,  the  several  images  re- 
fracted through  the  prism  would  92 
overlap    one    another   at   their 
edges,  as  is  shown  in  fig.  92, 
each  colour  would  mingle  with    Impure  spectrum  obtained  by  the 
the  adjoining  one,  and  no  part 

of  the  spectrum  thus  obtained  would  exhibit  a  pure 
and  homogeneous  colour.  By  the  adoption  of  a  slit 
placed  parallel  to  the  angle  of  the  prism  this  evil  is 
to  a  great  extent  avoided,  and  in  point  of  fact  the 
spectrum  becomes  purer  and  the  dispersion  into  homo- 
geneous colour  more  complete  the  narrower  the  slit 
is  made. 

57.  As  white  light  is  a  mixture  of  the  various 
coloured  rays  of  the  spectrum,  these  must  conversely  be 
capable  of  being  combined  together  again  to  form  white 
light.  In  fact,  if  the  spectrum  be  allowed  to  fall  upon  the 
anterior  surface  of  a  large  lens  I  (fig.  93),*  all  the  rays 


Combination  of  the  colours  of  the  spectrum  to  form  white  light. 

proceeding  from  a  point  s  of  the  posterior  surface  of  the 
prism  unite  in  the  conjugate  point  /,  and  thus  throw 
upon  a  paper  screen  placed  at  this  point  an  image  of 


The  lens  must  be  achromatic. 


120 


OPTICS. 


FIG.  94. 


the  posterior  surface  of  the  prism  in  which  the  dis- 
persed rays  reunite.  This  image  is  white. 

It  immediately  ceases  to  be  white  however  if  one 
of  the  colours  be  abstracted  from  the  mixture.  If,  for 
example,  the  red  and  orange  rays  are  received  on  a 

prism  of  small  refracting  angle 
(fig.  94)  placed  behind  the  lens, 
these  are  deflected  and  produce 
at  the  side,  at  n,  a  reddish 
coloured  image.  The  image  /, 
in  which  still  the  yellow,  green, 
blue,  and  violet  rays  unite,  now 
exhibits  a  greenish  mixed  colour. 
These  two  reddish  and  greenish 
colours  must  when  mingled  to- 
gether (which  can  be  immedi- 
ately effected  by  removing  the 
prism  p)  obviously  produce  white 
light  again,  for  the  one  contains 

exactly  those  kinds  of  rays  required  by  the  other  to 
form  that  mixture  which  we  call  white.  Two  colours, 
which  in  this  way  form  white  by  their  union,  are 
called  complementary  colours.  As  the  prism  is  gradually 
moved  along  the  whole  length  of  the  spectrum  other 
colours  constantly  become  deflected  to  the  side,  and 
the  images  n  and  /  exhibit  successively  an  entire 
series  of  complementary  pairs  of  colours.  By  this 
means  we  learn  that  red  and  green,  yellow  and  blue, 
greenish  yellow  and  violet  tints  are  complementary  to 
one  another. 

In  order  to  mingle  any  two  simple  colours  a  screen 
with  two  vertical  slits  a  and, b  is  placed  before  the  lens 
i  (fig.  95),  the  distance  and  breadth  of  which  can 


Complementary  colours. 


DISPERSION   OF   COLOUR.  121 

be  altered  at  pleasure ;  it  follows  then  that  only  those 
parts  of  the    spectrum  are  combined  in  the  image*/ 
which  have  traversed  these  slits.     From  red  and  violet 
a  full   purple-red  is   thus 
obtained,  from  blue-violet 
and  orange  a  delicate  rose 
colour,  but  out   of  Indigo 
blue    and   yellow  —  white. 
Thus  in  order  to  obtain  the 
impression'  of  white  for  our 
eyes,    the    co-operation  of 
all  the  colours  of  the  spec- 
trum is  by  no  means  neces- 
sary, but  as  Helmholtz  first 

Combination  of  two  homogeneous  colours. 

showed,  white  may  be  pro- 

iduced  by  the  combination  of  only  two  homogeneous 
/  colours.  Amongst  the  homogeneous  colours  comple- 
mentary to  each  other  are  red  and  greenish  blue,  ora.nge 
and  clear  blue,  yellow  and  dark  blue,  and  greenish 
yellow  and  violet.  It  is  generally  found  that  for  each 
part  of  the  spectrum  from  the  red  end  to  the  beginning 
of  the  green,  there  is  a  complementary  spot  in  that  part 
of  the  spectrum  which  extends  from  the  commencement 
of  the  blue  to  the  violet  end.  The  green  spectrum  colour 
alone  possesses  no  simple  colour,  but  only  a  compound 
one  complementary  to  it,  namely,  purple. 

58.  The  re  fraction  of  com  pound  light  is  in  all  in  stances 
accompanied  by  dispersion.  If  for  example  a  beam  of  solar 
rays  be  allowed  to  fall  upon  a  prism,  this  is  not  merely 
deflected,  but  becomes  at  the  same  time  spread  out 
like  a  fan,  producing  upon  a  screen  a  solar  spectrum 
which  is  composed  of  the  same  colours  in  the  same 


122  OPTICS. 

sequence  as  the  spectrum  of  the  glowing  electric  carbop 
points."* 

The  dispersion  of  the  colours  of  the  solar  rays  is 
exhibited  on  the  mopt  magnificent  scale  by  Nature  her- 
self in  the  splendid  phenomenon  of  the  rainbow.  A 
rainbow  is  seen  whenever  the  observer  turns  his  back 
to  the  unclouded  sun  and  looks  towards  falling  rain. 

The  following  experiment  will  explain  the  mode  in 
which  the  rainbow  is  formed  by  refraction  and  internal 
reflexion  of  the  solar  rays  in  the  spherical  rain-drops. 

Upon  a  glass  sphere  k  filled  with  water  and  having 
a  diameter  of  4  centim.  (H  in.)  a  beam  of  solar  light  of 
equal  or  greater  diameter  than  the  sphere  is  allowed  to 
strike  horizontally,  and  there  is  then  seen,  upon  a  large 
screen  s  s  placed  in  front  of  the  sphere,  and  perforated  in 
its  centre  to  allow  the  passage  of  the  incident  rays,  ar- 
ranged concentrically  to  the  aperture  and  at  a  distance 
from  it  which  is  nearly  equal  to  that  of  the  sphere  from 
the  screen,  a  beautifully  coloured  circle,  in  fact  a  circular 
spectrum,  the  colours  of  which  are  arranged  concen- 
trically and  in  such  a  manner  that  the  red  is  outside 
and  the  violet  on  the  inside.  At  a  still  greater  distance 
from  the  centre  of  the  screen  a  second  similar  but 
much  fainter  circle  is  observed,  the  colours  of  which 
however  succeed  one  another  in  the  inverse  order, 
the  red  appearing  on  the  inside  and  the  violet  at  the 
outer  periphery. 

The  first  circle  is  formed  by  rays  which  have  pene- 

*  Tf  it  be  required  to  investigate  the  phenomena  of  refraction  apart 
irom  the  influence  of  dispersion,  homogeneous  light  must  be  employed.  On 
this  ground,  in  investigating  refraction  through  a  prism,  the  aperture  of 
the  Heliostat  was  formerly  (§  35)  closed  with  a  red  glass  which  only 
permits  red  and  nearly  homogeneous  light  to  pass  through  it. 


DISPERSION   OF   COLOUR. 


123 


FIG.  96. 


trated  the  sphere  and  have  been  reflected  from  its 
posterior  surface,  emerging  again  at  its  anterior  surface. 
By  reason  of  this  twofold  re- 
fraction and  a  single  internal 
reflexion,  as  is  shown  in  fig. 
96,  the  rays  experience  a 
deflection  from  their  original 
course  which  differs  with  the 
distance  of  the  incident  rays 
from  the  central  ray.  By 
the  central  ray  we  mean  that 
which  passes  through  the 
centre  of  the  sphere ;  it  is 
reflected  upon  itself  at  the 
posterior  surface,  and  con- 
sequently undergoes  no  re- 
fraction. As  we  pass  from 
this  central  ray  the  refraction 
of  the  rays  begins  to  increase 
until  at  a  certain  distance  it  reaches  its  maximum  ; 
from  this  point  onwards  to  the  outermost  rays  striking 
the  margin  of  the  sphere  the  amount  of  refraction 
again  diminishes. 

The  most  strongly  refracted  rays  which  strike  the 
screen  at  the  periphery  of  the  circle  cause  an  illumina- 
tion that  far  exceeds  that  of  the  single  point  in  the  interior 
of  the  circular  area.  If  we  commence  with  the  rays  which 
undergo  the  greatest  amount  of  refraction  and  pass  either 
to  the  central  ray  or  to  the  marginal  rays,  the  refraction 
alters  at  first  very  slowly  and  subsequently  very  quickly. 
Consequently  the  rays  which  adjoin  those  that  are  most 
refracted  associate  themselves  with  the  la,tter  after  their 
emergence  and  augment  their  light.  Those  rays,  on 


Refraction  and  internal  reflexion  in  a 
rain-drop. 


1 24  OPTICS. 

the  other  hand,  that  fall  near  to  one  another  on  other 
parts  of  the  watery  sphere  emerge  after  the  second  re- 
fraction at  a  distance  from  each  other,  and  are  incapable 
of  producing  any  well-marked  illumination  upon  the 
screen. 

If  the  experiment  with  homogeneous  light  be  re- 
peated, the  aperture  of  the  Heliostat  being  covered  with, 
for  example,  a  red  glass,  the  image  upon  the  screen  is 
reduced  to  a  feebly  illuminated  circular  area,  which  is 
surrounded  by  a  very  bright  circular  line.  The  greatest 
deflection  for  the  red  rays  amounts  to  somewhat  more 
than  42°  (the  angle  between  o  k  and  k  I)  ;  the  other 
colours,  in  consequence  of  their  greater  refrangibility, 
approximate  again  more  to  the  direction  o  k  of  the 
incident  rays,  and  produce  circles  the  radii  of  which  are 
successively  smaller  in  the  order  of  their  refrangibility. 
The  deflection  of  the  violet  rays  amounts  to  about  a 
degree  less  than  that  of  the  red.  The  direct  white 
light  of  the  sun  must  therefore  produce  the  circular 
spectrum  which  is  seen  on  the  screen. 

The  second  iridescent  circle  is  caused  by  rays  which, 
as  is  shown  in  fig.  97,  have  been  twice  refracted  and 
FIG.  97.  twice  reflected  from  within.       The  least 

refraction  to  which  such  rays  are  liable 
amounts  to  about  51° ;  for  the  red  rays 
somewhat  less,  for  the  violet  somewhat 

\/l_y    more.        This    least    refraction     corre- 

.  sponds  to  the  second  circle,  the  brilliancy 

Refraction  and  double 

internal  reflexion  in  of   which,  on  account  of  the  repeated 

a  rain-drop. 

reflexion,  is  very  naturally  considerably 
smaller  than  that  of  the  former. 

Every  falling  rain-drop  acts  in  exactly  the  same 
manner  as  the  sphere  filled  with  water.  An  observer 


DISPERSION   OF   COLOUR. 


125 


FIG.  98. 


at  o  (fig.  98),  looking  at  falling  rain  with  his  back  to 
a  brilliant  sun,  perceives  therefore  the  light  once  re- 
flected in  the  interior  of 
the  drops,  but  only  in 
sufficient  strength  from 
such  drops  as  are  distant 
about  an  angle  of  42° 
from  the  point  of  the  sky 
opposite  to  the  sun.* 
The  rays  coming  from 
other  drops  continue 
their  course  past  the  eye 
unseen.  Since  the  drops 
A  A'  which  remit  the  red 
rays  toward  0  are  some- 
what more  distant  from 
the  point  8  than  the 


o<X 


X 


B' 
A 


Mode  of  formation  of  the  rainbow. 


drops  BB',  from  which 
the  less  strongly  refrac- 
ted violet  light  proceeds, 
the  observer  perceives  around  the  central  point  S  the 
circle  described,  in  which  the  colours  of  the  spectrum 
are  arranged  concentrically  from  without  inwards  in 
the  order  of  their  refrangibility.  This  constitutes 
the  primary  rainbow. 

The  much  fainter  secondary  or  subsidiary  rainbow 
is  distant  about  an  angle  of  51°  from  the  point  8.  It  is 
produced  by  the  rays  which,  after  being  twice  refracted 
and  twice  reflected,  have  undergone  the  least  possible 
deflection  in  the  rain-drops  ;  and  the  reason  that  the 


It  is  that  point  where  the  shadow  of  the  head  of  the  observer  would 
fall  if  the  earth  did  not  binder  it. 


126  OPTICS. 

colours  are  arranged  in  it  in  inverted  order — the  red 
being  internal  and  the  violet  external — is  easy,  from 
what  has  just  been  stated,  to  understand. 


APPENDIX   TO   CHAPTER  VIII. 

ON    THE    THEORY    OF    THE    RAINBOW. 

IN  fig.  99  the  circle  may  represent  a  sphere  of  water  or  a 
drop  of  rain.  If  OS  be  the  straight  line  drawn  irom  the  central 
point  of  the  drop  0  to  the  sun,  the  line  SA  parallel  to  it  will 
represent  a  ray  of  the  sun  striking  the  drop  at  the  point  A.  If 
the  radius  0  A  be  prolonged  to  L,  the  angle  L  A  S  or  the  angle 
equal  to  it,  A  0  S,  is  the  angle  of  incidence  (i)  of  the  ray  S  A.  A 
part,  A  B,  of  this  ray  penetrates  the  drop  under  an  angle  of  re- 
fraction r,  and  becomes  at  Z?,  where  it  strikes  the  posterior  surface 

FIG.  99. 


E/         'M 

Refraction  and  internal  reflexion  in  a  drop  of  water. 

under  the  angle  of  incidence  A  B  0  =  r,  partially  reflected 
inwards,  B  (7,  and  returns  lastly,  after  it  has  suffered  some  loss 
by  reflexion,  inwards  at  the  point  C  of  the  anterior  surface  of 
the  sphere,  into  the  air  under  the  angle  of  refraction  M  C  E  —  i. 
Let  the  ray  C  E  which  has  been  twice  refracted  and  once  reflected 
towards  the  interior  be  more  particularly  considered. 


DISPERSION   OF   COLOUE.  127 

The  angle  d,  which  corresponds  to  the  difference  between  the 
emerging  ray  C  E  and  the  direct  rays  from  the  sun,  results  in 
the  drawing  from  the  prolongation  of  the  lines  S  A  and  C  E  to 
thoir  decussation  in  D.  The  point  D  must  obviously  lie  on  the 
prolongation  of  the  radius  0  J5,  which  divides  the  whole  figure 
symmetrically,  and  consequently  bisects  the  angle  of  refraction 
d.  From  the  triangle  A  B  Z),  in  which  the  angle  A  D  B  =  ^  d 
and  B  A  D  =  i  —  r  are  opposite  to  the  external  angle  A  B  0  =  r, 
we  perceive  fit  once  that  there  is  the  following  relation  be- 
tween the  sevcrn)  angles  of  deflection,  incidence,  and  refraction  — 
L  d  +  f  -  r  =  r  ; 


comes  U<  the  same  thing, 

d  =  2  (2r—  i). 

This  expression  shows  how  the  angle  of  deflection  varies  with 
angles  of  incidence  and  of  refraction  ;  that  is  to  say,  with  the 
point  where  the  incident  ray  strikes  the  anterior  surface  of  the 
drop.  The  median  ray  S  0,  for  example,  which  strikes  the  sur- 
face of  the  qphere  perpendicularly  at  P,  is  reflected  upon  itself 
and  undergoes  no  deflection.  'Ihe  ray  C  E}  on  the  other  hand, 
which  entered  the  drop  at  the  point  A,  diverges  considerably 
from  its  original  direction  S  A.  Thus  it  comes  to  pass  that  the 
innumerable  parallel  rays  that  fall  upon  the  upper  part  PA  of 
the  droj>r  emerge  divergingly  in  various  directions  from  its  lower 
part  P  C.  The  eye  of  an  observer  standing  at  a  great  distance 
and  i«>oking  towards  the  lower  part,  P  C,  of  the  sphere,  in  general 
therefore  receives  only  a  very  faint  impression  of  light  because 
almo.'t  all  the  rays  proceeding  from  this  point  pass  by,  and  only 
a  few  reach  him. 

A  stronger  impression  of  light  can  only  be  perceived  in  "the 
event  of  there  being  some  point  upon  the  anterior  surface  of  the 
drop  in  the  vicinity  of  which  the  incident  parallel  rays  are  so 
refracted  that  after  having  left  the  sphere  they  still  continue  their 
c.ourse  together  in  the  direction  of  their  emergence,  so  that, 
instead  of  a  single  ray,  a  beam  of  light  composed  of  a  large 
number  of  nearly  parallel  rays  reaches  the  eye,  exciting  it  to  a 
livelier  sensation  of  light. 
10 


1 28  OPTICS. 

In  order  to  discover  this  point,  supposing  it  to  exist,  let  a  rny 
be  considered  which  strikes  the  sphere  very  near  to  the  point  A. 
To  this  the  angle  of  incidence  i  +  a  corresponds,  which  differs  only 
by  the  very  small  amount  a  from  that  of  the  ray  S  A.  Coin- 
cidently,  however,  with  the  angle  of  incidence  the  angle  of  refrac- 
tion also  undergoes  a  small  alteration,  /3,  and  becomes  r  +  /3.  In 
consequence  of  this,  the  deflection  d  must  also  change  to  a  small 
amount  and  obtain  a  new  value  d'.  The  relation  above  found 
must,  however,  still  always  remain  between  these  altered  values ; 
that  is  to  say,  it  must  happen  that 

d  =  2  (2r  +  2/3-i-o), 
or  that  d  =  2  (2r-t)  +  2  (2ft  -  a). 

If  this  new  value  of  the  deflection  be  now  compared  with  the 
former  one,  we  perceive  that  the  two  values  are  equal  to  each 
other,  when 

n  =  2/3. 

Hence,  in  order  that  two  neighbouring  incident  rays  should  un- 
dergo the  same  deflection  by  the  drop  of  water,  that  is  to  say, 
should  emerge  from  it  parallel  to  each  other,  it  is  necessary  that 
the  small  alteration  which  the  angle  of  incidence  undergoes  in. 
passing  from  one  ray  to  another  be  twice  as  great  as  the  corre- 
sponding alteration  of  the  angle  of  refraction. 

Fig.  100  will  serve  to  show  how  the  determination  of  the 
position  of  the  point  on  the  periphery  of  the  sphere  in  which  this 
condition  is  fulfilled  is  effected. 

The  smaller  of  the  two  concentric  circles  represents,  as  in  the 
preceding  figure,  the  circumference  of  the  drop. 

Jn  order  to  obtain  the  angle  of  refraction  corresponding  to 
the  angle  of  incidence  A  0  M  =  i,  in  accordance  with  what 
lu'.s  been  already  stated  respecting  the  law  of  refraction,*  a 
second  circle  is  to  be  constructed  around  the  same  centre,  the 
radius  of  which  is  greater  in  the  proportion  of  n  to  1  (n  re- 
presenting the  index  of  refraction  of  water).  Supposing  the  radius 
of  the  first  circle  to  be  unity,  that  of  the  second  will  equal  ?i,  and 
if  we  now  draw  through  A  the  straight  line  Q,  B  parallel  to  0  Mt 

*  See  Appendix  to  Chapter  V. 


DISPERSION   OF   COLOUR. 


129 


and  join  the  point  B  where  it  cuts  the  circumference  of  the  larger 
circle  with  the  centre  0,  BOM  will  represent  the  angle  of  re- 
fraction r  corresponding  to  the  angle  of  incidence  z. 

The  segments  of  the  circle  MA  and   M  (7,  which"  correspond 
to  these  angles  upon  the  circumference   of  the  circle  having  a 


Theory  of  the  rainbow. 


radius  of  1  may  serve  as  a  measure  of  them.  If  the  same  con- 
struction be  repeated  for  the  larger  angle  of  incidence  a  0  M 
—  i  +  a  around  the  same  segments  of  the  circle  A  a  =  a,  whilst 
g  6  is  drawn  parallel  to  0  M,  we  obtain  the  angle  of  refraction 
b  0  M  or  c  0  M,  which  exceeds  the  foregoing  to  the  small  extent 
C  c  =  /3.  The  arcs  A  a  and  C  c  thus  represent  the  corresponding 
alterations  of  the  angles  of  incidence  and  of  refraction,  and  being 
very  small  segments  of  the  circumference  of  the  circle,  they  may, 
without  any  very  great  error,  be  regarded  as  rectilinear  just  as 
the  arc  B  /;,  which  corresponds  to  the  small  angle  of  the  central 
point  C  0  c  =  /3  upon  the  circle  having  a  radius  w,  and  is  there- 
fore equal  to  ?i/3. 

If  from  the  points  A  and  B  we  let  fall  the  perpendiculars  A  k 
and  B  /,  and  from  0  the  perpendicular  0  q  upon  the  straight  line 
q  6,  we  can  easily  see  that  the  small  triangles  A  k  a  and  B  I  b  are 


130  OPTICS. 

fiimilar  to  the    corresponding   and    larger   triangles  A  Q  0   and 
B  QO.     Hence  it  follows  that 

A  a      AO         .  Bb       BO 

~     *  3    =    '  or> 


if  we  indicate  A  Q  by  v,  B  Q  by  r,  the  equal  segments  A  k  and 
B  I  by  m,  and  conceive  that  A  0  =  1,  B  0  =  n,  yl  a  =  a,  and 
Ptb  —  nft\  then, 

«  1  T  nfi  n 
—  =  —  ,  and  _!_  =  -, 
m  v  m  v 

or  also,  since  in  the  second  equation  the  factor  n  appears  upon 
both  sides  and  may  therefore  be  eliminated, 

f--1,  and  £  =  1. 

m      v          m       v 

From  these  two  equations  it  results  that  the  ratio  of  the  two 
augments  a  and  /3  assumes  the  following  form  :  — 

_  =  _  ;  that  is  to  say, 
P        v 

since  the  coincident  changes  of  the  angles  of  incidence  and  refrac- 
tion are  constantly  to  one  another  as  B  Q  :  and  A  Q  ;  and  a  is  twice 
as  great  as  /3,  therefore  B  Q  must  be  twice  as  great  as  A  Q,  or 
the  point  A  must  bisect  the  line  B  Q.  In  order,  consequently,  to 
discover  the  point  A  upon  the  periphery  of  the  sphere  of  water 
the  neighbourhood  of  which  the  parallel  rays  of  the  sun  are  so 
refracted  that  they  leave  the  sphere  as  a  parallel  beam,  the  fol- 
lowing construction  must  be  applied.  Around  the  circle  which 
represents  the  circumference  of  the  drop  and  the  radius  of  which 
is  taken  as  =  1,  a  second  circle  is  described  with  the  radius  n, 
n  being  regarded  as  the  index  of  refraction  of  water  ;  we  now 
draw  the  diameter  R  0  R'  parallel  and  the  diameter  POP'  per- 
pendicular to  the  direction  of  the  incident  rays,  and  amongst  the 
innumerable  lines  which  may  be  conceived  as  drawn  from  the 
points  of  the  circumference  of  the  second  circle  parallel  to  P  0  P' 
to  meet  It  0  R'  ,  seek  for  that  one  which  is  bisected  by  the  first 
circle.  The  middle  point,  which  must  obviously  lie  in  the  cir- 
cumference of  the  first  circle,  is  the  point  required.  In  order 


DISPEKSION   OF  COLOUK.  131 

to  attain  this  end  with  certainty,  the  search  must  not  be  entered 
upon  thoughtlessly,  but  must  be  proceeded  with  systematically.  If 
the  collective  series  of  lines  B  Q  be  conceived  to  be  bisected,  in- 
numerable middle  points  are  obtained,  amongst  which  is  neces- 
sarily the  one  sought  for,  which,  as  a  whole,  is  always  a  curved 
line  passing  through  the  terminal  point  P  of  the  second  diameter, 
and  through  the  bisecting  point  AT  of  the  radius  0  R'.  This 
curved  line  is  obviously  an  ellipse,  the  greater  semidiameter  of 
which  OP  =  w,  and  the  smaller  semidiameter  0  N  =  ±  n.  This 
can  be  easily  constructed,  and  is  seen  in  the  right  half  of  fig.  100. 

As  the  point  looked  for  must  lie  upon  this  ellipse  as  well  as 
upon  the  circle  with  the  radius  1,  it  is  found  immediately  as  the 
point  of  intersection  ( A'}  of  these  two  curved  lines.  The  angle 
of  incidence  sought  for  A'  0  M'  =  t,  as  well  as  the  corresponding 
angle  of  refraction  B'  0  R'  =  r,  may  now  be  obtained  either 
directly  from  the  figure  by  measurement,  or  more  exactly  by 
calculation. 

If  it  be  admitted  for  the  sake  of  argument  that  the  sun  emits 
only  the  simple  yellow  light  of  Sodium,  the  index  of  refraction  of 
water  for  this  kind  of  light  is  exactly  |.  If  this  value  be  taken 
as  a  base  for  the  construction,  we  find  i}  =  59°  24',  r,  =  40° 
12',*  and  since  d{  is  equal  to  2  (2r{  —  i\)  the  corresponding  de- 
flection is 

dl  =  42°. 

In  this  direction  only  does  a  beam  of  nearly  parallel  rays 
emerge  from  the  drop,  which,  because  they  remain  together  in 
the  long  path  to  the  eye,  penetrate  it  together,  and  hence  occasion 
a  lively  sensation  of  light. 

These  rays,  which  emerge  parallel  to  each  other  from  the 
drop,  are  distinguished  from  the  rest  in  another  point  of  view. 
Their  deflection  is  the  maximum  which  the  sphere  of  water  is 
capable  of  producing  on  rays  of  a  definite  refrangibility.  We 
can  easily  convince  ourselves  of  this  by  the  following  considera- 
tion. At  the  point  A,  which  corresponds  to  the  angle  of  inci- 

*  It  is  remarkable  that  for  the  index  of  refraction  |  the  angle  of  inci- 
dence and  triple  the  angle  of  refraction  together  from  two  right  angles, 
that  is  to  say,  «,  +  3r,  =  180°. 


OPTICS. 

dence  ilt  as  we  have  seen,  the  alteration  a  of  the  angle  of 
incidence  is  equal  to  twice  the  alteration  of  the  angle  of  refraction 
or  to  2/3.  On  the  other  side  of  the  point  A,  with  the  greater 
angle  of  incidence  z'j  +  a',  to  which  also  a  greater  angle  of  refrac- 
tion r,  4-  j3'  corresponds,  a'  is  greater  than  2/3,  because  the  same 
also  B  Q  (fig.  100)  is  greater  than  2 A  Q.  The  deflection  of 
this  ray  is  consequently 

d'  =  2  (2r,  +  2/3'  -  i,  -  a') 

or, 

d'  =  di  +  4/3'  -  2a'. 

Since  u'  is  greater  than  2/3',  and  therefore  also  2a'  is  greater 
than  4/3'  we  have,  in  order  to  obtain  rf',  to  subtract  more  than 
to  add,  consequently  d'  is  smaller  than  dl.  On  this  side  of  the 
point  A,  the  angle  of  incidence  is  smaller  than  il7  it  is  z\  —  a'v 
and  the  corresponding  angle  of  refraction  rt  —  /3".  The  deflec- 
tion d"  which  this  ray  experiences  is  therefore 

d"  =  2  (2rL  -  2/3"  -  i,  +  a") 
or, 

d"  =  dl  -  4/3"  +  2«". 

But  since  because  B  Q  is  here  less  than  2  A  Q,  a"  is  also  less 
than  2/3",  we  must  subtract  a  greater  amount  than  we  add,  and 
d"  is  thus  less  than  dlt  The  deflection  d}  which  the  parallel  rays 
experience  on  their  emergence,  is  thus  in  fact  the  maximum 
which  can  occur  with  single  internal  reflexion. 

In  fig.  100  the  determination  of  the  point  A  is  only  effected 
for  the  single  ratio  of  refraction  $ ;  for  every  other  index  of 
refraction  we  must  construct  according  to  the  same  rules  another 
external  circle  and  another  ellipse,  and  thus  convince  ourselves 
that  the  less  refrangible  rays  experience  a  greater  refraction 
(—  42°  13'),  and  the  more  refrangible  violet  rays  a  less  deflec- 
tion (=41°  14'). 

The  evidence  above  adduced  constitutes  the  basis  on  which 
the  explanation  of  the  primary  rainbow  is  founded. 

In  regard  to  the  secondary,  a  brief  explanation,  after  what  has 
just  been  said,  ia  all  that  is  necessary.  Since  the  deflection  which 


DISPERSION   OF   COLOUR.  133 

a  ray  of  light  has  experienced  after  double  internal  reflexion  is 
expressed  by 

d  =  180°  -  2  (3r  -  i) 

the  condition  a  =  3/3  must  be  present  for  parallel  emerging  rays. 
We  find  therefore  the  point  of  incidence  which  satisfies  this 
condition  if  we  construct  an  ellipse  in  fig.  100,  of  which  the 
greater  axis  likewise  —  »,  but  the  smaller  axis  —  ^  n.  By  a 
quite  similar  train  of  reasoning  it  may  then  easily  be  shown  that 
the  deflection  (=  51°  for  n  =  £)  which  corresponds  to  this  point 
t«  the  minimum  which  can  occur  with  double  internal  reflexion. 


134  OPTICS. 


CHAPTER    IX. 

ACHROMATISM. 

59.  A  PURE  spectrum  of  solar  light  is  obtained 
by  allowing  it  to  pass  through  the  vertical  slit  of  the 
Heliostat,  and  arranging  the  lens,  prism,  and  screen 
as  before.  At  first  sight  the  solar  spectrum  does  not 
appear  to  differ  from  that  of  the  electric  light;  the 
succession  and  division  of  the  colours,  the  degree  of 
refraction  and  length  of  bands  of  colour  is*  the 
same  in  both  cases.  On  closer  inspection,  however,  of 
the  brightly  illuminated  surface,  we  perceive  a  great 
number  of  dark  lines,  which  are  disposed  perpen- 
dicularly to  the  long  axis  of  the  spectrum,  and  conse- 
quently parallel  with  the  slit.  These  dark  lines,  the 
majority  of  which  are  extremely  fine,  though  some  are 
very  well  marked,  were  first  observed  by  Wollaston 
(1802),  and  were  subsequently  more  exactly  investigated 
by  Fraunhofer  (1814).  The  last-named  observer,  from 
whom  they  have  received  the  name  of  Fraunhofer's 
Lines,  distinguished  eight  prominent  lines  by  the  letters 
A  to  H.  The  line  A  lies  at  the  extremity  of  the  dark 
red ;  B  and  G  in  the  middle  of  the  red  ;  D  between  the 
orange  and  yellow ;  E  in  the  green  ;  F  in  the  inter- 
mediate colour  between  green  and  blue  ;  G  in  the  dark 
blue,  and  H  towards  the  end  of  the  violet  (see  fig.  106). 

*  For  the  same  prisms. 


ACHROMATISM.  135 

The  spectrum  of  solar  light  is  consequently  not 
continuous,  like  that  of  white-hot  charcoal,  but  there 
are  small  interspaces  which  appear  to  us  as  fine  dark 
lines.  From  the  presence  of  these  spaces  we  must  con- 
clude that  the  homogeneous  kinds  of  light  correspond- 
ing to  them  are  deficient  in  the  light  of  the  sun. 

The  lines  of  Fraunhofer  constitute  well-defined 
marks,  within  the  gradual  transitions  of  colour  of  the 
spectrum  which  always  correspond  to  the  same  homo- 
geneous kinds  of  light,  and  afford  us  the  means  of 
defining  each  part  of  the  spectrum,  and  of  discovering 
it  again  at  all  times  with  certainty.  How  very  useful 
these  points  are  in  our  enquiries  will  be  seen  as  we 
proceed. 

60.  Up  to  the  present  time  a  prism  of  flint  glass 
has  always  been  used  for  the  production  of  the  spectrum. 
But,  in  order  to  compare  the  dispersion  of  colour  of  vari- 
ous substances,  three  prisms  must  successively  be  taken, 
each  of  which  possesses  a  refracting  angle  of  60°,  namely, 
one  of  flint  glass,  one  of  crown  glass,  and  finally,  a 
hollow  prism  filled  with  water.  The  first  thing  that 
is  observed  is  that  the  spectra  which  they  throw  are 
refracted  laterally  to  different  extents.  That  caused  by 
the  flint  prism  is  deflected  to  the  greatest  degree,  that 
by  the  crown  glass  to  a  less  extent,  and  that  by  the 
water  prism  least  strongly.  The  spectra  vary  also  con- 
siderably in  length ;  the  spectrum  thrown  by  the  flint 
glass  is  nearly  double  as  long  as  that  thrown  by  the 
water  prism. 

We  may  now  ask:  Is  the  stronger  dispersion  of 
colour  exhibited  by  the  flint-glass  spectrum  simply  the 
consequence  of  its  greater  refracting  power,  or  does  the 
flint  glass,  in  virtue  of  its  material  qualities,  possess  a 


136  OPTICS. 

greater  power  of  dispersion  than  the  other  two  sub- 
stances ?  In  order  to  answer  this  question,  we  must 
compare  the  lengths  of  the  spectra  of  equal  refraction 
with  one  another.  A  flint-glass  prism  may  easily  be 
prepared  which  shall  cause  the  same  refraction  in  any 
particular  homogeneous  kind  of  light,  as,  for  example, 
in  the  rays  which  correspond  to  Fra.unhofer's  line  D,  as 
a  prism  of  crown  glass  of  60°.  Such  a  prism  of  flint 
glass  must  obviously  have  a  refracting  angle  of  less 
than  60°,  and  one  in  fact  that  amounts  to  about  52°. 
The  crown-glass  prism  of  60°,  and  the  flint-glass  prism 
of  52°,  give  spectra  in  which  the  line  D  undergoes  the 
same  amount  of  deflection.  Notivithstanding  this,  the 
flint  spectrum  from  B  to  H  is  nearly  double  as  long  as 
that  of  the  crown  glass.  From  this  it  may  be  concluded 
that  the  power  of  dispersion  of  the  flint  glass  is  almost 
double  (speaking  exactly,  1-7  times)  as  great  as  that  of 
crown  glass. 

Two  similar  prisms  made  of  the  same  material  (for 
example,  two  prisms  of  60°  composed  of  crown  glass)  of 


Combination  of  two  similar  prisms  without  deflection  and  without  dispersion. 

course  produce  equal  refraction  and  equal  dispersion  of 
colour,  that  is  to  say,  equal  length  of  the  spectrum. 
If  they  be  placed,  as  in  fig.  101,  behind  one  another 
with  their  refracting  angles  in  opposite  directions, 
the  second  one  restores  to  the  original  condition  the 
refraction  as  well  as  the  dispersion  of  colour  caused  by 
the  first.  The  white  beam  of  light  which  penetrates 


ACHROMATISM.  137 

the  first  emerges  from  the  second  as  white  light  again, 
coursiug  parallel  to  its  original  direction,  and  producing  a 
white  image  of  the  slit  upon  the  screen.  The  combina- 
tion of  the  two  prisms  acts  like  a  thick  plate  of  glass 
with  parallel  surfaces,  which  causes  neither  refraction 
nor  dispersion.  What  will  occur,  we  may  now  ask,  if  a 
crown-glass  prism  of  60°  be  placed  behind  a  flint-glass 
prism  of  52°  with  the  refracting  angle  reversed  ?  The 
deflection  of  the  Fraunhofer's  line  D  disappears  ;  but 
since  it  causes  nearly  twice  as  long  a  spectrum  as 
the  crown-glass  prism,  the  dispersion  of  colour  is  not 
removed,  but  becomes  reversed.  We  perceive  there- 
fore upon  the  screen  in  the  direction  of  the  direct  rays 
a  spectrum  of  about  the  same  length  as  that  caused  by 
the  crown-glass  prism,  but  with  the  succession  of  colours 
inverted. 

In  making  observations  upon  the  spectrum  formed 
by  a   prism,    it    is    frequently   inconvenient    that   the 

spectrum  should  be  deflected  so  far  to  one  side. 

1*1 

FIG.  W0. 


Combination  of  a  crown  and  of  a  flint-plass  prism  causing 
dispersion  but  no  deflection. 

The  experiment  just  made,  however,  shows  how 
the  spectrum  may  be  obtained  in  the  direction  of  the 
incident  rays,  and  to  avoid  the  necessity  of  putting  the 
prisms  into  position  on  every  occasion,  they  may  be 
cemented  together  by  a  transparent  substance  (Canada 
balsam).  Such  a  combination  is  called  a  direct  vision 
prism.  Such  combinations  of  prisms  are  usually  made 
up  of  three  (fig.  103)  or  of  five  (fig.  104)  prisms  ;  one 
flint  and  two  crown,  or  two  flint  and  three  crown. 


138 


OPTICS. 


Now  a  prism  of  flint  glass  which  throws  just  as  long 
a  spectrum  as  a  prism  of  crown  glass  must  have  its 


FIG.  103. 


FIG.  104. 


Showing  combinations  of  prisms  which  cause  110  deflect  ion  (a  vision  direcle). 

refracting  angle  about  half  the  size  of  that  of  the  latter. 
It  causes,  however,  considerably  less  deflection.  If  we 
combine  therefore  two  such  prisms  (a  crown-glass 
prism  of  about  60°  and  a  flint-glass  prism  of 
about  30°)  placing  them  in  opposite  positions  (fig. 
105),  the  second  abolishes  the  dispersion  of  colour 


FIG.  105 


Combination  of  a  crown  andnint-glass  prism,  with  deflectiuii 
but  without  refection  (an  achromatic  prism). 


produced  by  the  first.  On  the  other  hand,  it  diminishes 
but  does  not  completely  remove  the  deflection.  We 
obtain  therefore  upon  the  screen  a  white  image  of  the 
slit  deflected  to  one  side.  In  the  combination  of  the  two 
prisms  we  thus  possess  a  prism  causing  no  dispersion  of 
colour,  or  an  achromatic  prism. 

Thus  it  appears  that  one  of  the  two  actions  of  a 
prism,  deflection  and  dispersion,  can  be  abolished  with- 
out interference  with  the  other,  nevertheless  only  by  a 
combination  of  at  least  two  prisms  made  of  different 
materials.  Two  prisms  made  of  the  same  kind  of  glass 


ACHROMATISM.  139 

either  abolish  both  actions  simultaneously  (fig.  101),  or 
leave  both  intact. 

61.  The  different  power  of  dispersion  possessed  by 
various  substances  shows  that  an  influence  is  exerted  by 
the  material  of  which  the  prism  is  composed  upon  the 
light  traversing  it.  This  action  may  be  still  further 
followed  if  spectra  of  equal  length  from  B  to  H  (fig.  106) 
of  a  crown-glass  prism  of  60°,  and  a  flint-glass  prism  of 

FIG.  106. 


Spectrum  thrown  by  crown  glass  and  by  flint  glass. 

30°,  be  compared,  for  which  purpose  the  lines  of  Fraun- 
hofer,  which  always  correspond  to  the  same  homogeneous 
tints  of  colour,  serve  as  excellent  guides.  By  their 
position  in  the  two  spectra  it  is  rendered  evident  that 
the  less  refrangible  rays  are  more  closely  approximated 
in  passing  through  the  flint  glass,  whilst  the  more  re- 
frangible are  separated  further  from  one  another  than 
by  the  crown  glass ;  so  that  although  the  total  disper- 
sion of  the  two  prisms  (that  is  to  say,  the  length  of  their 
spectra  between  B  and  H)  is  exactly  the  same,  their 
dispersion  is  different.  If,  therefore,  as  previously 
pointed  out,  they  be  added  together,  the  second  cannot 
completely  abolish  the  dispersion  of  the  former,  and 
the  -combined  prism  is  not  completely  achromatic.  The 
very  small  dispersion  of  colour  that  still  remain^  can 


140  OPTICS. 

only  be  removed  by  a  properly  selected  thicker  prism, 
composed  again  of  a  third  substance.  In  the  mean- 
time, however,  it  is  so  small  that  it  may  be  usually 
neglected. 

62.  The  laws  of  light  in  regard  to  lenses,  of  which 
a  knowledge  has  already  been  acquired,  are  only  strictly 
accurate  under  the  presumption  that  we  are  dealing 
with  homogeneous  light ;  as,  for  example,  with  the 
light  of  the  Sodium  flame.  In  consequence  of  the 
unequal  refrangibility  of  the  different  coloured  rays,  an 
ordinary  lens  has  a  different  focal  distance  for  each 
kind  of  light — the  focus  of  the  violet  rays  (v,  fig.  107) 
being  nearer  to  the  lens  than  that  of  the  red  rays  (r). 


FIG.  107. 


Dispersion  of  colour  of  a  lens. 

It  is  impossible  for  the  rays  emanating  from  aluminous 
point  of  white  or  parti-coloured  light  to  be  reunited 
again  into  one  point ;  the  images  thereon  are  therefore 
not  sharply  defined,  but  surrounded  by  faint  coloured 
rings.  A  telescope  or  microscope  with  such  a  lens  as  an 
objective  would,  on  account  of  the  indistinctness  of  its 
images,  be  almost  valueless.* 

The  prevention  of  the  dispersion  of  lenses  is  always 
therefore  an  object  of  solicitude  in  practical  optics  ; 
and  before  the  solution  of  the  problem  was  discovered  by 

*  "We  can,  however,  obtain  well-defined  images  with  a  microscope  thus 
dispersing  light,  if  we  illuminate  the  object  with  homogeneous  light,  such 
for  instance  as  that  of  the  Sodium  flame. 


ACHKOMATiSM.  141 

Hall  in  1 733,  and  by  Dollond  in  1757,  it  was  impossible 
to  construct  serviceable  telescopes,  and  it  was  found 
necessary  to  take  refuge  in  the  less  powerfully  luminous 
reflecting  telescopes. 

That  &  single  lens  can  never  be  free  from  dispersion 
is  obvious  ;  but,  on  the  other  hand,  it  is  possible  to 
combine  two  lenses  of  such  nature  that  each  is  capable 
of  mutually  compensating  for  or  destroying  the  dis- 
persion of  the  other.  A  method  by  which  the  desired 
result  may  be  obtained  is  indicated  by  the  production 
of  the  achromatic  prism. 

In  order  to  remove,  namely,  the  dispersion  of  colour 
of  a  lens,  we  place  a  second  lens  of  opposite  action 
immediately  behind  it  which  possesses  the  same  dis- 
persion of  colour  but  causes  a  different  amount  of  refrac- 
tion ;  that  is  to  say,  has  another  focal  distance. 

We  add,  for  example,  to  a  convex  crown-glass  lens 
a  concave  flint-glass  lens  ;  and 
in  order  that  both  should  effect  FlG- 108- 

equal  but  opposite  dispersion  of     A^^^          ^llrf 
colour,  the  virtual  focal  distance     J^t^^ 
of  the  latter  must  be  about  twice  Achromatic  lens. 

as  great   as   the  real  focal  dis- 
tance of  the  former.     Their  combination  then  gives  an 
achromatic  lens   (fig.   108),   which  unites   all  the  rays 
emitted  from  a  white  point  into  a  white  image- point 
again. 

For  the  reason  formerly  mentioned  in  speaking  of 
the  achromatic  prism,  we  do  not  even  here  obtain 
entire  freedom  from  colour.  The  amount  still  remain- 
ing is,  however,  extremely  small. 

63.  The  first  compound  achromatic  lenses  con- 
structed on  this  principle  were  discovered  by  experi- 


142 


OPTICS. 


meiit.  The  greatest  perfection  can,  however,  only  be 
obtained  if,  instead  of  the  uncertain  method  of  trial, 
direct  calculation  be  made  of  the  most  favourable  form 
for  both  the  flint  and  crown  glass.  In  order  to  do  this, 
however,  an  exact  knowledge  of  the  indices  of  refraction 
of  the  kinds  of  glass  for  the  various  homogeneous  rays 
of  light  is  required.  The  indices  of  refraction  in  regard 
to  the  red,  yellow,  green,  and  other  rays,  were  laid 
down  long  ago,  but  on  account  of  the  gradual  tran- 
sition of  the  rays  into  each  other  rendering  a  sharp 
definition  of  their  limits  impracticable,  the  numbers 
discovered  were  inexact.  But  when  Fraunhofer  em- 
ployed the  dark  lines  named  after  him  as  fixed  points, 
he  was  able  to  measure  exactly  the  indices  of  refraction 
for  determinate  homogeneous  rays,  and,  proceeding  on 
this  information,  to  construct  achromatic  objectives  for 
telescopes  that  have  not  hitherto  been  surpassed  in  the 
perfection  of  their  performance.  The  method  we  have 
hitherto  pursued  in  order  to  throw 
the  spectrum  as  an  object  upon  a 
screen  is  excellently  adapted  to  ex- 
hibit a  large  number  of  its  peculi- 
arities. If,  however,  it  be  desired 
to  make  a  special  study  of  its  char- 
acters, and  to  make  measurements, 
the  direct  method  of  observation  ap- 
plied by  Fraunhofer  has  the  advan- 
tage. 

In  this  method  a  telescope  (fig. 
109)  is  Placed  immediately  behind 
the  prism,    the    objective    lens    of 
which,  whilst  it  receives  the  rays  emerging  from  the 
prism,  throws  a  spectrum  near  its  focus,  which  is  then 


FIG.  109. 


ACHROMATISM. 


143 


seen  with  tlie  ocular  as  through  a  lens.  The  Fraunhofer 
lines  can  thus  be  seen  with  extraordinary  definition  and 
clearness.  The  direct  method  of  observation  through 
a  telescope  also  has  the  advantage  that  it  does  not 
require  nearly  so  much  light  as  the  projected  image 
method. 

If  a  divided  circle  be  combined  with  the  observing 
telescope  (fig.  109),  we  are  able,  by  directing  the  cross 
threads  successively  to  each  Fraunhofer's  line,  to  mea- 
sure accurately  the  slightest  differences  in  their  posi- 
tion, and  then  in  accordance  with  the  method  above 
given  to  determine  the  corresponding  index  of  refraction. 
The  indices  of  refraction  of  some  of  the  more  important 
substances  for  the  principal  Fraunhofer  lines  as  thus 
obtained  are  given  in  the  accompanying  little  Table  : — 


B 

C 

D 

E 

F 

G 

H 

Water  

1-3309 

1-3P17 

1-3336 

1-3359 

1-3378 

1-3413 

1-3442 

Alcohol  .... 
Carbon  bisulphide  . 
Crown  glass,  No.  9  . 
Flint  glass,  No.  13  . 
Flint  glass  of  Merz 

1-3628 
1-6182 
1-5258 
1-6277 
1-7218 

J-3633 
1-6219 
1-5268 
1-6297 
1-7245 

1-3654 
1-6308 
1-5296 
1-6350 
1-7321 

1-3675 
1-6438 
1-5330 
1-6240 
1-7425 

1-3696 
1-6555 
1-5361 
1-6483 
1-7521 

1-3733 
1-6799 
1-5417 
1-6603 
1-7725 

1-3761 
1-7019 
1-5466 
1-67H 
1-7895 

As  each  substance  has  a  special  index  of  refraction 
for  each  kind  of  ray,  it  is  necessary  to  point  out  in 
every  statement  respecting  an  index  of  refraction,  which 
homogeneous  ray  is  meant,  and  when,  as  in  the  indices 
of  refraction  given  at  p.  60,  such  a  precise  statement 
is  neglected,  the  observation  is  only  approximate,  and 
refers  to  the  middle  rays  between  D  and  E. 

Any  Theodolite  may  be   used  for  the  measurement, 

upon  Fraunhofer's  plan,  of  prismatic  deflection,  and  in 

order  that  the  prism  should  follow  the  rotation  of  the 

telescope,  it  must  be  placed  upon  a  small  table  attached 

11 


144  OPTICS. 

to  the  objective  end  of  the  telescope.  The  refracting 
angle  of  the  prism,  which  must  be  known  for  the  calcu- 
lation of  the  index  of  refraction,  is  determined  by  means 
of  the  reflecting  goniometer,  p.  34. 

64.  The  determination  of  the  index  of  refraction  can 
be  much  more  conveniently  effected  by  means  of  Meyer- 
stein's  Spectrometer,  a  representation  of  which  is  given 
in  fig.  110.  The  observing  telescope  is  here  directed  to 
the  centre  of  the  horizontal  divided  circle,  and  is  sup- 
Era,  no. 


Spectrometer. 

ported  on  horizontal  arms  connected  with  the  vertical 
axis  of  the  divided  circle.  This  axis  rotates  in  the  bore 
of  a  metal  column  supported  by  three  screws  giving  off 
above,  three  horizontal  arms.  Two  of  these,  which  are 
opposite  to  each  other,  carry  the  indicators  (nonia)  by 
means  of  which  the  rotation  of  the  divided  circle  is  read 
off;  the  third  arm  carries  a  telescope  directed  towards 
the  centre  from  which  the  ocular  has  been  removed, 
and  is  replaced  by  a  vertical  slit.  This  slit  is  situated 
in  the  focus  of  the  objective  lens,  so  that  the  rays  pro- 


ACHROMATISM.  145 

ceeding  from  it  strike  the  prism  as  a  parallel  beam,  and 
traverse  it  at  right  angles  to  its  refracting  edge,  that 
is  to  say,  each  passes  through  a  principal  section.  Were 
this  condition  not  fulfilled,  the  prism  would  produce,  in 
consequence  of  the  rays  directed  obliquely  to  its  principal 
section,  a  confusion  of  the  image  of  the  slit  which 
would  make  itself  disturbingly  perceptible  in  the  spec- 
trum as  a  curvature  of  the  Fraunhofer's  lines.  Whilst 
by  means  of  the  '  slit-tube,'  the  slit  can  be  withdrawn 
to  any  distance,  it  confers  upon  the  Spectrometer  the 
advantage  of  being  applicable  to  the  investigation  of  the 
weaker  lights. 

To  obtain  parallel  rays  when  employing  the  method 
of  Fraunhofer,  the  distance  of  the  Theodolite  from 
the  slit  must  be  increased  as  far  as  possible;  011  this 
account  it  is  especially  adapted  for  sunlight,  for  when 
the  distance  is  considerable  the  feebleness  of  artificial 
sources  of  light  is  not  sufficient ;  with  the  Spectrometer, 
on  the  other  hand,  the  source  of  light  can  be  brought 
immediately  in  front  of  the  slit,  and  consequently 
weaker  sources  of  light  can  be  made  the  subject  of 
experiment.  When  the  observing  tube  and  the  slit 
tube  have  exactly  the  same  direction,  the  slit  is  seen  at 
the  decussation  of  the  threads  of  the  former,  and  the 
indicator  points  to  zero  upon  the  divided  circle. 

We  now  place  the  pi  ism  (or  rather  the  small  tablet 
supported  by  three  screws  on  which  it  stands)  in  the 
middle  of  the  instrument,  upon  a  second  smaller  hori- 
zontal divided  circle,  the  vertical  axis  of  which  turns  in 
a  socket  formed  by  a  bore  in  the  axis  of  the  greater 
circle.  We  must  now  turn  the  observing  tube,  and 
with  it  the  great  circle,  to  one  side,  in  o  der  to  perceive 
the  deflected  image  of  the  slit,  or  rather  its  spectrum ; 


1 46  OPTICS. 

by  turning  the  small  circle  the  prism  can  easily  bo 
brought  into  the  position  of  smallest  deflection,  the 
amount  of  which  can  be  read  off  after  accurate  focussing 
by  the  indicator  of  the  large  divided  circle. 

The  smaller  divided  circle  has  still,  however,  a 
second  important  use.  It  forms,  if  we  allow  the  greater 
circle  to  remain  fixed,  with  the  slit  and  observing  tube 
together,  a  Eeflecting-goniometer  (p.  34).  We  can  there- 
fore with  all  necessary  exactitude  determine  by  means 
of  this  instrument,  the  Spectrometer,  the  two  qualities 
which  are  required  for  the  calculation  of  the  index  of 
refraction,  namely,  the  smallest  deflection  and  the 
refracting  angle  of  a  prism. 


APPENDIX  TO  CHAPTER  IX. 

ACHROMATIC    LENSES. 

WHEN  two  thin  lenses  are  placed  one  immediately  behind 
the  other,  as  in  fig.  108,  the  deflection  which  they  produce  in 
a  point  at  any  distance  k  from  the  common  axis  is  equal  to 
the  sum  of  the  deflections  which  each  of  the  lenses  would  have 
itself  effected.  If  F  therefore  indicates  the  focal  distance  of  the 
compound  lens/,  that  of  the  first,  and  (p  that  of  the  second  lens, 

k         k   .    k  1         1         1 

r~7^''~r~?** 

The  focal  distances/  and  0  of  the  two  separate  lenses  are, 
however,  different  for  different  coloured  rays,  for  we  obtain  (ac- 
cording to  Equation  I.  p.  92,  for  example),  the  focal  distance  for 
red  rays 


ACHROMATISM.  147 

for  violet,  on  the  other  hand, 


fv 
where  n'  and  n'  indicate  the  indices  of  refraction  of  crown  glass 

r  v 

for  red  and  violet  rays,  and  r^  and  r2  the  radii  of  curvature  of 
crown-glass  lenses. 

In  the  same  way  we  have 


and 


(I  + 1), 

\P\         P*' 


where    the    corresponding    quantities   for   flint-glass    lenses   are 
indicated  by  n"  and  ft",  /oj  and  j02.      If  the  combination  of  the 

r  v 

two  lenses  for  red   and  violet  possess  the  same  focal  distance 
the  two  lenses  must  be  such  that 

I  +  J.  =  1. 

/,   t,  f,   t>: 

With  the  aid  of  this  equation  and  the  expressions  above  given 
for  the  several  focal  distances,  the  radii  of  curvature  which  must 
be  given  to  the  two  lenses  in  order  to  obtain  an  achromatic 
system  may  be  calculated  with  facility. 


148 


OPTICS. 


CHAPTER  X. 

SPECTRUM     ANALYSIS. 

65.  IF  instead  of  the  measurement  of  indices  of 
refraction  the  observation  and  comparison  of  the  spectra 
proceeding  from  various  sources  of  light  be  the  subject 

FIG. ill. 


Bunsen's  spectroscope. 


of  enquiry,  the  divided  circle  of  the  spectrometer  may 
be  dispensed  with ;  and  the  instrument  thus  simplified 
constitutes  Bunsen's  Spectroscope  (fig.  Ill),  in  which  the 
slit  tube  A,  the  prism  P,  and  the  observing  tube  B,  are 


SPECTRUM  ANALYSIS.  149 

all  arranged  just  as  in  the  spectrometer.  In  order, 
however,  to  obtain  the  means  of  measurement  within  the 
limits  of  the  spectrum  without  a  divided  circle,  a  very 
ingenious  apparatus  has  been  introduced.  A  third  tube, 
C  (the  scale- tube),  has  at  its  outer  end,  at  *,  a  small 
photographed  scale  with  transparent  divisions,  whilst 
ett  the  inner  end  is  a  lens  which  is  placed  at  about  its 
focal  distance  from  the  scale.  The  scale  is  illuminated 
by  means  of  a  lamp  or  candle.  The  scale-tube  is  so 
placed  that  the  rays  of  light  that  proceed  from  the 
scale  and  emerge  parallel  to  the  axis  of  the  tube  are 
reflected  at  the  anterior  surface  of  the  prism  in  the 
direction  of  the  observing  tube.  The  observer  looking 
into  the  telescope  sees  therefore  coincidently  with  the 
spectrum  of  the  light  F,  the  image  of  the  scale,  which 
may  be  used  as  a  measure. 

As  the  rays  are  deflected  from  their  original  direc- 
tion by  the  prism,  the  observing  tube  in  the  spectro- 
scope just  described  must  be  so  placed  in  regard  to  the 
slit-tube  as  to  form  an  angle  which  is  about  equal  to 
the  smallest  deflection  of  the  middle  rays.  The  source 
of  light  to  be  investigated  cannot  therefore  be  looked  at 
directly,  a  circumstance  which  renders  the  arrangement 
of  the  instrument  difficult  and  its  management  somewhat 
awkward.  The  direct  vision  or  rectilinear  spectroscope  (a 
vision  directe)  which  instead  of  a  single  prism  contains 
a  combination  of  prisms,  so  that  there  is  no  deflection, 
is  free  from  this  inconvenience  (fig.  104).  To  this 
class  belongs  Hoffman's  Spectroscope,  and  the  little  (only 
8^  in.  long)  pocket  Spectroscope  of  Browning. 

66.  By  means  of  the  spectroscope  the  spectra  of 
the  glowing  vapours  formerly  thrown  upon  the  screen 
can  be  very  conveniently  observed  (objective!^  But 


150  OPTICS. 

whilst  for  those  researches  the  dazzling  light  of  the 
electric  flame  was  requisite,  the  flame  of  a  Bunsen's 
burner  is  now  sufficient,  at  least  for  the  light  metals 
(fig.  1).  Instead  of  the  metal  itself,  some  of  its 
chemical  combinations,  or  so-called  salts,  are  usually 
employed.  A  small  quantity  of  such  a  salt  is  melted 
[it  the  extremity  of  a  fine  platinum  wire,  and  intro- 
duced into  the  external  hottest  part  of  the  feebly 
luminous  flame.  The  salt  is  decomposed  by  the  heat ; 
the  flame  is  saturated  with  the  vapour  of  the  metal  now  , 
set  free,  and  is  tinted  with  a  colour  characteristic  of 
the  metal.  With  a  little  Sodium  chloride  (common  f " 
salt),  for  example,  we  obtain  the  homogeneous  yellow 
light  of  Sodium  ;  salts  of  Lithium  and  Strontium  colour 
the  flame  of  a  carmine  red  tint;  salts  of  Potassium 
clear  violet ;  salts  of  Barium  green  ;  and  salts  of 
Calcium  yellowish  red.  Analysts  had  no  doubt  long 
employed  these  characters  to  demonstrate  the  presence 
of  the  above  metals,  but  the  colour  of  the  flame  continued 
to  be  an  uncertain  means  of  recognition  until  pris- 
matic decomposition  was  applied  as  a  means  of  in- 
vestigation. It  was  almost  impossible,  for  example, 
with  the  naked  eye  to  distinguish  between  the  red 
flame  of  Lithium  and  that  produced  by  Strontium,  but 
if  the  two  are  looked  at  through  the  spectroscope  they 
exhibit  perfectly  distinct  spectra,  which  are  exhibited 
on  the  Spectrum  plate  (see  Frontispiece,  Nos.  6  and  8). 
If,  again,  a  specimen  of  Sodium  salt  with  which  only  a 
trace  of  Lithium  is  mingled  be  examined,  the  presence 
of  the  latter  cannot  be  recognised  with  the  naked  eye, 
because  its  feeble  red  stain  is  completely  overpowered 
and  concealed  by  the  brilliant  yellow  of  the  Sodium. 
The  spectroscope,  however,  shows  distinctly  the  red  li.ie 


SPECTEUM   ANALYSIS.  151 

of  Lithium  close  to  the  yellow  Sodium  line,  each  in  its 
place,  thus  disclosing  the  chemical  composition  of  the 
substance  in  question. 

This  qualitative  method  of  chemical  analysis  is  termed 
spectrum  analysis,  and  although  the  spectra  of  some 
coloured  flames  had  been  known  for  some  time,  and  their 
applicability  as  chemical  tests  recognised,  Bunsen  and 
Kirchhoff  were  the  first  who  laid  down  the  scientific 
grounds  on  which  alone  a  method  of  investigation 
could  be  raised,  and  who  must  therefore  be  regarded  as 
the  true  discoverers  of  spectrum  analysis.  Bunsen  and 
Kirchhoff  showed  first  that  the  positions  which  the  bright 
lines  of  the  spectrum  occupy  are  independent  of  the 
temperature  of  the  flame  ;  in  fact,  that  the  same  red 
colour  is  obtained  and  the  same  two  lines,  a  red  and  a 
reddish  yellow,  are  seen  in  the  spectroscope  whether 
the  Lithium  chloride  be  volatilised  in  the  flame  of  a 
Bunsen's  burner  or  in  the  much  hotter  flame  of  the 
oxyhydfogen  blowpipe.  It  is  to  be  noted  that  the 
brilliancy  of  the  several  lines  increases  with  increasing 
temperature,  and  thus  it  may  happen  that  by  means  of 
intense  heat  lines  come  into  view  which  at  lower  tem- 
peratures are  too  feeble  to  be  perceived.  If,  for  example, 
Lithium  be  volatilised  in  the  electric  flame,  a  blue  line  is 
visible  in  its  spectrum,  which  occupies  exactly  the  same 
position  as  the  blue  line  of  Strontium.  In  the  flame  of 
the  Bunsen's  burner  it  exhibits  only  the  two  above- 
named  lines.  Moreover,  the  two  observers  just  men- 
tioned demonstrated  that  different  combinations  of 
the  same  metals  give  invariably  the  same  spectrum,, 
whence  the  conclusion  is  irresistible  that  the  lines  seen 
in  any  instance  may  be  regarded  as  positive  evidence 
of  the  actual  presence  of  the  metals  in  question. 


152  OPTICS. 

The  spectrum  method  of  analysis  is  distinguished 
from  ordinary  chemical  methods  by  its  extreme  delicacy. 
The  three- millionth  part  of  a  milligramme  of  a  salt  of 
Sodium,  an  imperceptible  particle  of  dust  to  the  naked 
eye,  is  yet  capable  of  colouring  the  flame  yellow  and  of 
giving  the  yellow  line  of  Sodium  in  the  spectroscope. 
More  than  two  thirds  of  the  surface  of  the  earth  are 
covered  by  sea,  which  contains  Sodium  chloride,  or 
common  salt.  When  waves  are  raised  by  the  storm 
and  their  foaming  summits  are  carried  away,  fine 
particles  of  salt  are  mingled  with  the  air  and  carried  far 
over  the  land  ;  common  salt  is  consequently  distributed 
through  the  whole  atmosphere  in  the  form  of  a  fine 
dust.  On  account  of  this  almost  constant  presence  of 
Sodium  chloride,  it  is  scarcely  possible  to  obtain  a 
flame  which  does  not  exhibit  the  yellow  line  of  Sodium. 
It  is  only  necessary  to  strike  a  handkerchief  upon  the 
table,  or  to  close  a  book  sharply,  to  make  the  dust 
which  escapes  colour  the  adjoining  Bunsen's  flame 
yellow,  and  to  make  the  Sodium  line  appear  in  the 
spectroscope.  Moreover,  in  the  representation  of  the 
spectra  of  different  metals  by  means  of  the  electric 
lamp,  they  can  never,  as  has  been  seen,  be  obtained  com- 
pletely free  from  the  Sodium  line. 

The  extraordinary  sensitiveness  of  the  spectrum 
method  of  analysis  led  its  celebrated  discoverers,  Bun- 
sen  and  Kirchhoff,  to  the  discovery  of  two  new  alkaline 
metals  that  had  previously  escaped  the  notice  of 
chemists,  Caesium  and  Rubidium,  the  compounds  of 
which  occur  only  in  very  small  quantities  in  minerals 
and  mineral  waters.  These  spectra  are  represented  in 
Nos.  2  and  3  of  the  Spectrum  plate.  Subsequently, 
Crookes,  from  the  spectroscopic  examination  of  the 


SPECTRUM  ANALYSIS.  153 

crust  formed  in  the  lead  chambers  of  a  sulphuric  acid 
manufactory,  discovered  the  lead-like  metal  Thallium 
(No.  10),  and  Reich  and  Eichter  also  discovered,  by 
means  of  spectrum  analysis,  in  certain  ores  of  zinc  the 
zinc-like  metal  Indium. 

67.  The  spectrum  method  of  analysis  just  described 
has  been  chiefly  applied  to  the  recognition  of  the 
alkalies  and  alkaline  earths,  for  the  heat  of  a  Bunsen's 
burner  is  insufficient  to  volatilise  the  heavy  metals  and 
obtain  their  vapour  in  a  glowing  state.  To  effect  this 
we  must  seek  other  means,  and  we  possess  them  in  the 
electric  lamp,  which  may  be  used  in  order  to  exhibit  the 
spectra  of  several  of  the  heavy  metals  upon  a  screen. 
If  a  fragment  of  zinc  be  volatilised  between  the  carbon 
poles  a  series  of  beautifully  coloured  striae  are  seen, 
especially  one  red  and  several  blue.  If  now  a  fragment 
of  brass,  which  is  composed  of  zinc  and  copper,  be 
added,  in  addition  to  the  zinc  lines  the  group  of  green 
lines  peculiar  to  copper  are  immediately  observed.  By 
the  addition  of  a  little  silver  the  spectrum  of  this 
metal  appears,  which  also  exhibits  a  group  of  green 
lines,  but  these  are  easily  distinguishable  by  their 
position  from  those  of  the  copper.  It  is  observable 
that  the  inevitable  Sodium  line  is  a  constant  accompani- 
ment of  all  these  experiments. 

As  a  powerful  galvanic  battery  is  required  for  the 
production  of  the  electric  arc  of  light,  spectrum  analysis 
in  its  application  to  the  discovery  of  the  heavy  metals 
would  prove  very  troublesome  were  there  no  more  con- 
venient means  of  converting  the  metals  into  luminous 
vapours.  For  the  purposes  of  subjective  observation 
through  the  spectroscope  the  ordinary  electric  spark  is 
sufficient,  or  still  better  the  spark  of  a  powerful  induction 


154 


OPTICS. 


FIG.  112. 


apparatus,  which  by  means  of  a  few  galvanic  cells  can  be 
maintained  in  unbroken  activity.  This  apparatus  is  ex- 
hibited in  fig.  112,  but  a  detailed  description  of  its  con- 
struction and  mode  of  action  would  here  be  out  of  place. 
It  is  enough  to  say  that  if  the  conducting  wires  of  the 
galvanic  battery  are  fastened  down  by  the  binding  screws 
C  and  D,  electric  sparks  succeed  each  other  in  rapid 
succession  between  the  poles  A  and  B,  which  can  be  still 
further  intensified  by  the  introduction  of  a  Leyden  jar. 
These  sparks  contain  particles  of  the  pole  in  the  condi- 
tion of  glowing  vapour.  If  the  poles,  therefore,  consist 
of  the  metal  to  be  examined,  which  may  either  be  used 
in  the  form  of  a  wire  or  in  the  form  of  irregular  fragments 

fixed  by  means  of  clips, 
the  sparks  will  exhibit 
the  corresponding  spec- 
trum of  the  metal  when 
seen  through  the  spec- 
troscope. 

This  method  of  ob- 
servation demonstrates 
that  the  representation 
of  spectra  upon  the 
screen  was  inexact;  each 
of  the  bright  lines  now 
shows  itself  to  be  composed  of  a  number  of  extremely 
fine  lines  which,  owing  to  the  poor  definition  of  the 
objective  image,  previously  coalesced  into  a  more  or 
less  broad  band.  Owing  to  the  great  number  of  fine 
blight  lines,  the  spectra  of  the  heavy  metals  are  very 
complex.  In  the  spectrum  of  iron,  for  example,  more 
than  450  bright  lines  have  been  counted. 

68.  In   the  light  of  the  electric  spark,  not  only  do 


Induction  apparatus. 


SPECTRUM  ANALYSIS.  155 

particles  of  metal  detached  from  the  poles   glow,  but 
also  particles  of  the  gas  through  which  the  spark  passes. 
In   the   method  of  observation  just  described,  there- 
fore, the  metallic  spectrum  is  not  pure,  but  is  mingled 
with  the  spectrum  of  the  atmosphere. 
This  admixture  cannot  however  oc- 
casion any  error,  providing  the  spectra 
which  glowing  gases  themselves  give 
are  known. 

In  order  to  render  a  gas  incande- 
scent the  discharge  of  an  induction 
apparatus  is  allowed  to  pass  through 
a  so-called  Geissler's  tube  (fig.  113), 
which  contains  the  gas  in  question 
in  a  rarefied  state.  The  two  ends 
of  the  tube  present  dilatations  into 
which  platinum  wires  are  fused. 
These  wires  are  connected  with  the 
poles  of  an  induction  apparatus,  and 
immediately  a  beautiful  stream  of 
light  traverses  the  interior  of  the 
tube,  the  colour  of  the  light  varying 
with  the  nature  of  the  contents.  If 
the  tube  contain  hydrogen  the  middle 
constricted  portion  shines  with  a 
splendid  purple-red,  the  brilliancy  of 
which  is  nevertheless  too  feeble  to 

Geissler's  spectrum  tube. 

permit  its  spectrum  to  be  projected 
upon  a  screen  so  as  to  be  visible  at  any  distance. 
If  the  tube  be  looked  at  through  the  spectroscope 
the  light  of  the  hydrogen  a.ppears  to  be  composed 
of  three  homogeneous  kinds  of  light :  a  red,  a  bluish 
green,  and  a  violet  line  coming  into  view.  (See  Plate 


156  OPTICS. 

of  Spectra,  No.  12.)  A  tube  filled  with  rarefied  nitrogen 
shines  with  a  peach-blossom  colour,  but  gives  a  far  more 
complex  spectrum  than  that  of  hydrogen;  for  in  the 
red,  orange,  yellow,  and  green,  numerous  closely  approxi- 
mated bright  lines  are  seen  separated  from  each  other 
by  slender  dark  lines ;  in  the  blue  and  violet,  on  the 
other  .  hand,  there  are  broad  bright  bands  which  are 
sharply  defined  towards  the  less  refrangible  side,  but  are 
gradually  shaded  off  towards  the  refrangible  side. 
(No.  13.) 

Pliicker  and  Hittorf,  and  more  recently  Wiillner, 
have  demonstrated  that  in  this  method  of  observation 
different  spectra  are  obtained  with  the  same  gas,  if  the 
presence  of  the  gas  and  the  kind  of  electrical  discharge 
are  appropriately  altered.  If  with  the  induction  appa- 
ratus a  Leyden  flask  be  connected,  and  the  shock  thus 
intensified  be  transmitted  through  the  same  tube  con- 
taining nitrogen,  light  of  another  colour  may  be  ob- 
served to  be  emitted  from  it,  and  if  this  be  examined 
with  the  spectroscope  it  exhibits  a  spectrum  consisting 
of  many  sharply-defined  bright  lines.  A  Geissler's  tube 
filled  with  nitrogen  thus  gives  two  quite  distinct  spectra, 
according  to  the  kind  of  electrical  discharge.  With 
low  electric  tension  it  gives  the  spectrum  of  the  first 
order,  consisting  of  bright  striae  and  bands,  whilst  with 
high  tension  it  gives  the  spectrum  of  the  second  order, 
consisting  of  narrow  bright  lines.  Other  gases  behave 
in  a  similar  manner.  PliickeT  and  Wiillner  have  even 
shown  that  hydrogen,  under  increased  pressure  and  with 
electric  discharges  of  high  tension,  gives  a  continuous 
spectrum,  and  hence  emits  light  of  all  degrees  of  refran- 
gibility.  In  the  same  way  Frankland  has  observed  that 
a  flame  of  hydrogen  burning  in  oxygen  under  very  high 


SPECTRUM   ANALYSIS.  157 

pressure  emits  white  light,  which  gives  a  continuous 
spectrum.  Our  knowledge  of  the  processes  which  take 
place  in  Geissler's  tube  during  electrical  discharges  is 
still  too  imperfect  to  permit  the  conclusion  to  be  drawn 
from  the  phenomena  just  described  that  the  same  gas 
can  furnish  different  spectra.  It  is,  on  the  contrary, 
not  improbable  that  the  spectra  presenting  lines  (to 
which  the  above-mentioned  hydrogen  spectrum  belongs) 
characterise  the  simple  gases,  whilst  the  spectra  pre- 
senting bands  belong  to  certain  of  their  chemical 
compounds. 

69.  The  spectra  that  have  hitherto  been  considered 
may  be  arranged  in  the  three  following  classes  : — 

]  st,  Continuous  spectra,  like  those  of  the  glowing 
carbon  points  in  the  electric  lamp,  Drummond's  lime 
light,  the  magnesium  light,  white-hot  platinum,  iron 
in  -a  state  of  fusion,  and,  speaking  generally,  and  with 
bat  few  exceptions,  all  white-hot  solid  or  fluid 
bodies,  whatever  may  be  their  composition.  All  these 
exhibit  a  spectrum  which  on  beginning  to  be  luminous 
presents  the  extreme  red,  and  as  the  temperature  rises 
constantly  extends  towards  the  more  refrangible  end, 
and  finally  becomes  complete  and  continuous  when 
white  heat  is  attained.  The  flames  of  candles,  lamps, 
and  gas-burners  also  give  continuous  spectra,  for  they 
owe  their  brightness  to  the  particles  of  solid  carbon 
floating  in  them.  Finally,  to  this  group  belong  the 
above-mentioned  continuous  spectra  which  are  observed 
under  certain  circumstances  in  gases. 

2nd,  Spectra  which  present  a  number  of  bright 
lines  and  strice  on  a  dark  background.  These  are  peculiar 
to  glowing  vapours  and  gases,  each  chemical  element  and 
chemical  compound  having  its  own  characteristic 


158  OPTICS. 

spectrum.     It   is    this   which  constitutes  the  basis  of 
spectrum  analysis. 

3rd,  The  solar  spectrum  which  exhibits  a  large 
number  of  fine  dark  lines — the  lines  of  Fraunhofer — on 
a  bright  ground.  These  lines  are  perceived  by  means 
of  the  spectroscope  in  ordinary  daylight,  in  the  light 
of  the  moon,  and  in  that  of  the  planets,  and  hence  not 
only  in  the  direct  but  in  the  reflected  light  of  the  sun. 
The  fixed  stars,  as  independent  suns,  exhibit  spectra 
which  are  similar  but  not  identical  with  that  of  the 
sun.  The  circumstance  that  the  dark  lines  of  tho 
fixed  stars  are  not  exactly  coincident  with  those  of  the 
sun,  permits  the  conclusion  to  be  drawn  that  the  lines 
of  Fraunhofer,  or  at  least  a  large  number  of  them,  do 
not  proceed  from  any  action  of  the  atmosphere  of  our 
earth,  but  are  peculiar  to  the  solar  light  at  its  source. 
An  endeavour  must  now  be  made  to  obtain  more  exact 
information  in  regard  to  the  cause  leading  to  their 
production. 


SPECTRUM   ANALYSIS   OF  THE  SUN. 


159 


CHAPTER   XL 

SPECTRUM    ANALYSIS     OF     THE    SUN. 

9 

70.  FRAUNHOFER  first  observed  that  the  bright  yellow 
line  of  the  Sodium  flame  occupies  the  same  position  in 
the  spectrum  as  the  dark  line,  D,  of  the  solar  light. 
In  order  to  demonstrate  this,  a  right-angled  prism  (fig. 
114)  must  be  so  placed  in  front 
of  the  slit  which  has  hitherto  been 
employed  to  throw  the  spectrum, 
that  it  only  covers  the  lower  half  of 
the  slit.  From  the  side  B  the  light 
of  the  electric  arc,  saturated  with 
Sodium  vapour,  falls  upon  the 
prism,  arid  undergoing  total  re- 
flexion, is  deflected  by  the  oblique 
surface  to  the  slit,  whilst  the  sun's 
rays,  as  before,  penetrate  through 
the  upper  uncovered  part.  The  spectra  of  the  two  sources 
of  light  corresponding  to  the  two  halves  of  the  slit  are 
therefore  thrown  upon  the  screen,  one  being  immediately 
above  the  other,  permitting  them  to  be  conveniently  com- 
pared. It  will  then  be  seen  that  the  bright  Sodium  line 
forms  the  exact  continuation  of  the  dark  line  D  in  the 
solar  spectrum,,  and  the  conclusion  may  be  drawn  that  the 
Sodium  light  possesses  the  same  refrangibility  as  the 
12 


Action  of  the  comparison 
prism. 


160 


OPTICS. 


line  D.  The  '  Sodium  light'  and  c  the  D  light'  are  there- 
fore equivalent.  (See  Spectrum  Plate,  Nos.  1  and  5.) 

Such  a  comparing — or  comparison — prism  may  be 
applied  to  the  slit  of  any  spectroscope  (fig.  115.)  It 
permits  the  light  coming  from  any  source  to  be  looked 
at  coincideiitly  with  that  of  the  solar  spectrum,  one 
occupying  the  upper,  the  other  the  lower  half  of  the 
field  of  vision,  and  thus  permits  them  to  be  directly 
compared.  The  solar  spectrum,  owing  to  the  numerous 
fine  lines  it  exhibits,  may  be  taken  as  a  scale  by  which, 
all  others  may  be  measured. 

By  means  of  the  comparing  prism  it  may  be  demon- 
strated that  the  three  bright  lines  of  the  hydrogen 

Ito.  115. 


Comparing  prism  at  the  slit  of  the  spectroscope. 

flame  possess  exactly  the  same  refrangibility  as  three 
dark  lines  in  the  solar  spectrum.  The  red  line  occupies 
precisely  the  position  of  the  dark  solar  line  0;  the 
greenish  blue  corresponds  to  the  line  F,  and  the  dark 
blue  to  a  Fraunhofer's  line  which  lies  immediately  in 
front  of  G.  (See  the  Plate  of  Spectra,  Nos.  1  and  I:7.) 
Kirchhoif  in  like  manner,  in  endeavouring  to  deter- 
mine the  precise  position  of  the  bright  lines  of  metals, 
used  the  solar  spectrum  as  a  scale,  and  found  that  there 
were  Fraunhofer's  lines  which  corresponded  to  each  of 
the  iron  lines  he  had  observed.  The  coincidence  de- 


SPECTRUM  ANALYSIS   OF   THE  SUN.  161 

pcends  to  the  minutest  particulars  ;  the  more  brilliant 
a  bright  iron  line  appears  the  blacker  is  the  correspond- 
ing Fraunhofer's  line;  the  more  defined  is  the  line  of  the 
metal  the  more  definite  is  also  the  solar  line;  if,  011  the 
contrary,  it  be  faint  and  have  softened  edges,  there  is 
a  corresponding  indistinctness  in  the  solar  spectrum. 
Thus  every  bright  iron  line  (of  which  Angstrom  and 
Thalen  have  lately  counted  not  less  than  460),  has  its 
dark  counterpart  in  the  solar  spectrum.  The  exact 
coincidence  of  so  many  bright  iron  lines  with  dark  solar 
lines  cannot  be  accidental.  On  the  theory  of  probabili- 
ties millions  of  millions  might  be  wagered  to  one  that 
these  lines  have  a  common  origin,  or  in  other  words, 
it  is  almost  certain  that  both  kinds  of  lines  are  pro- 
duced by  the  glowing  vapour  of  iron. 

71.  How  does  it  happen,  however,  that  the  lines 
which  in  the  spectrum  of  a  glowing  vapour  appear 
bright  upon  a  dark  ground  are  seen  conversely  in  the 
solar  spectrum,  dark  upon  a  bright  ground.  A  few  ex- 
periments will  show  how  an  answer  to  this  question 
may  be  given.  The  continuous  spectrum  of  the  electric 
light  passing  between  the  carbon  points  is  projected 
upon  the  screen,  and  a  fragment  of  Sodium  is  placed 
in  the  cavity  of  the  lower  pole.  As  it  vaporises  it  in- 
vests the  white-hot  upper  carbon  point  with  a  sheath  of 
flame,  which  emits  the  well-known  homogeneous  yellow 
light.  But  there  may  now  be  seen  upon  the  screen  in 
the  continuous  spectrum  a  dark  line,  occupying  exactly 
the  position  where  before  was  the  bright  Sodium  line, 
and  where  it  now  again  immediately  appears  if  the 
carbon  poles  be  so  far  separated  that  the  light  of  the 
arc  of  flame  alone  reaches  the  prism. 

From  this  experiment  the  conclusion  may  be  drawn 


162 


OPTICS. 


TIG.  no. 


that  the  yellow  sheath  of  flame  permits  all  kinds  of  rays 
proceeding  from  the  white-hot  carbon  to  pass  easily 
through  it,  with  the  exception  of  that  kind  of  ray  which 
it  emits  itself.  This  is  completely  arrested  or  absorbed  ; 
in  other  words,  the  vapour  of  Sodium 
is  almost  opaque  for  rays  of  its  own 
kind,  whilst  it  is  perfectly  permeable 
to  all  other  kinds  of  rays. 

This  peculiarity  of  the  glowing 
vapour  of  Sodium  may  be  very  beauti- 
fully shown  by  means  of  an  apparatus 
constructed  by  Bunseii  (fig.  116). 
The  flask  A,  closed  by  an  elastic 
stopper  perforated  with  three  holes, 
contains  a  solution  of  common  salt 
(sodium  chloride)-,  besides  some  sul- 
phuric acid  and  zinc.  From  the  mix- 
ture hydrogen  gas  is  evolved,  which 
carries  with  it  small  droplets  of  the 
solution  of  common  salt.  Coal-gas 
is  conducted  into  the  flask  by  means 
of  the  bent  tube  e,  which,  after  admixture  with  the 
hydrogen  gas  containing  solution  of  common  salt, 
streams  out  through  the  tubes  a  and  c.  The  coal-gas 
flame  is  almost  non-luminous  per  se,  but  presents  a 
yellowish  tint  from  the  admixture  of  the  vapour  of 
Sodium,  and  becomes  mingled  with  air  before  under- 
going combustion  in  the  metal  chimneys  b  and  d.  The 
chimney  b  widens  like  an  inverted  cone  above,  and 
from  its  semicircular  slit-like  aperture  a  broad  ex- 
tremely hot  and  bright  Sodium  flame  is  emitted.  The 
other  chimney,  d,  is  funnel-shaped,  and  is  provided 
above  with  a  cover  having  an  aperture  in  the  centre. 


Bnnsen's  apparatus  for  the 
absorption  of  Sodium  light. 


SPECTEUM  ANALYSIS   OF  THE  SUN.  163 

Incomplete  combustion  takes  place  in  it,  and  a  feeble 
flame,  caused  bj  the  products,  appears  above  the  open- 
ing-.    This  small  Sodium  flame  appears  almost  perfectly 
dark  upon  the  bright  background   of  the         FlG.m. 
large  Sodium    flame ;   and  as  it  is  almost 
opaque  for  Sodium  light,  it  presents  us  with 
the  surprising  phenomenon  of  a  black  flame 
(fig.  117). 

It  cannot  be  doubted  that  the  flame  is 
not  in  itself  black,  but  emits  yellow  Sodium 
light,  as  indeed  may  be  immediately  seen  if 
the  large  flame  is  extinguished.  As  it  appears 
dark  upon  the  bright  background,  the  quan- 
tity of  light  which  it  emits,  together  with 
that  which  it  still  transmits  of  the  flame 
behind  it,  taken  together,  must  be  smaller  Absorption  of  the 
than  the  intensity  of  the  light  of  the  poste- 
rior flame.  It  must  thus,  consequently,  be  less  bright ; 
or,  since  the  intensity  of  light  rises  and  falls  with  the 
temperature,  less  hot  than  the  latter.  Owing  to  the 
peculiar  construction  of  these  metal  chimneys,  the  large 
flame  is  rendered  as  hot  as  possible,  whilst  the  small  one 
is  reduced  to  as  low  a  temperature  as  possible.  If  the 
anterior  flame  were  bright  enough  to  cover  or  even  to 
surpass  by  its  own  luminosity  the  loss  of  light  effected 
by  absorption,  the  small  flame  would  appear  as  bright 
or  even  still  brighter  than  its  background. 

The  dark  Sodium  line  also  which  has  heretofore  been 
seen  in  the  spectrum  is  not  absolutely  black;  it  still 
receives  the  sum  of  the  D-light  emitted  and  transmitted 
from  the  electric  arc.  It  appears,  however,  in  com- 
parison with  its  environment — the  brilliant  spectrum  of 
the  carbon  light--  dark. 


164  OPTICS. 

The  spectrum  of  Lithium  can  be  similarly  inverted 
to  that  of  Sodium.  For  if  a  salt  of  Lithium  be  placed 
on  the  inferior  charcoal  point  of  the  electric  lamp,  as 
well  as  a  fragment  of  Sodium,  Lithium  and  Sodium 
vapours  must  be  coincidently  present  in  the  flame ;  and 
there  is  now  seen  in  the  spectrum,  besides  the  dark 
line  D,  a  dark  line  in  the  red  exactly  in  the  position 
where  the  bright  red  Lithium  line  was  previously 
visible.  The  Lithium  vapour  thus  absorbs  just  those 
rays  which  it  itself  emits. 

The  law  which  has  been  demonstrated  in  the  case  of 
Natrium  and  Lithium  holds  good  generally.  Every  gas 
and  every  vapour  absorbs  exactly  those  kinds  of  rays  which 
it  emits  when  in  the  glowing  condition,  whilst  it  permits 
all  other  kinds  of  rays  to  traverse  it  with  undiminished 
intensity. 

This  capability  of  absorbing  remains  unaltered  under 
great  variations  of  temperature,  whilst  the  brilliancy 
of  the  light  emitted  rapidly  increases  or  diminishes  with 
the  temperature.  If  therefore  a  source  of  light  which 
gives  a  continuous  spectrum  be  looked  at  with  a  spec- 
troscope through  a  sheath  of  vapour,  various  appear- 
ances may  be  presented.  If  the  vapour  be  so  hot  that 
it  emits  more  light  than  it  annihilates  by  absorption, 
its  line-spectrum  will  be  seen  bright  upon  the  less  bright 
ground  of  the  continuous  spectrum.  If  its  capacity  of 
emitting  light  at  a  lower  temperature  be  just  sufficient 
to  cover  the  loss  of  light  caused  by  absorption,  a  con- 
tinuous spectrum  will  be  seen,  and  the  presence  of  the 
vapour  will  scarcely  be  recognisable.  Lastly,  if  at 
a  still  lower  temperature  the  emitted  light  be  insufficient 
to  make  up  for  that  lost  by  absorption,  the  lines  of  the 
vapour  will  appear  dark  upon  the  bright  ground  of  the 


SPECTKUM  ANALYSIS   OF  THE  SUN.  165 

continuous  spectrum,  or  in  other  words,  the  inverse 
spectrum  of  the  vapour  or  gaseous  body  is  developed. 

72.  The  inversion  of  gas  spectra  solves  the  enigma 
of  Fraunhofer's  lines,  and  at  the  same  time  gives 
an  insight  into  the  physics  of  the  sun.  The  sun, 
as  Kirchoff  maintains,  may  be  regarded  as  an  extremely 
hot  mass,  whose  glowing  white-hot  surface,  the  photo- 
sphere, emits  white  light,  and  in  and  by  itself  would 
give  a  continuous  spectrum.  Outside  of  the  photo- 
sphere and  surrounding  the  sun  is  an  atmosphere  of 
glowing  gases  and  vapours,  which  is  called  the  chromo- 
sphere ;  and  this  constituent,  though  of  lower  tempera- 
ture than  the  photosphere,  is  still  sufficiently  hot  to 
maintain  heavy  metals  in  the  state  of  vapour.  And 
since  the  light  of  the  photosphere,  before  it  reaches  the 
earth,  must  traverse  the  chromosphere,  it  is  subjected 
to  the  absorbing  action  of  the  gases  and  vapours  found 
in  it ;  and  it  is  to  this  action  that  the  lines  of  Fraunhofer 
owe  their  origin.  The  solar  spectrum  is  consequently 
to  be  regarded  as  resulting  from  the  juxtaposition  of 
the  inverted  spectra  of  all  those  substances  which  are 
contained  in  the  gaseous  state  in  the  solar  atmosphere. 

From  the  facts  already  mentioned  it  would  appear 
that  Hydrogen,  Sodium,  and  Iron  must  be  constituents 
of  the  solar  atmosphere.  Moreover,  exact  comparisons 
of  the  solar  spectrum  with  the  line- spectra  of  terrestrial 
substances  show  that  a  series  of  other  elements  *  exist 
in  the  sun.  Thus,  for  example,  the  two  lines  II  are 
produced  by  Calcium  vapour,  and  the  group  indicated 

*  The  presence  of  the  following  elements  has  been  demonstrated  with 
certainty  in  the  solar  atmosphere  : — Sodium,  Calcium,  Barium,  Magnesium, 
Iron,  Chromium,  Nickel,  Copper,  Zinc,  Strontium,  Cadmium,  Cobalt,  Hydro- 
gen, Manganese,  Aluminium,  and  Titanium. 


166  OPTICS. 

by  Fraunhofer  with  b  are  produced  by  the  vapour  of 
Magnesium.  The  line  G  depends  upon  Iron,  and  partly 
also  the  group  E.  The  lines  C  and  F  belong,  as  we 
already  know,  to  Hydrogen,  and  D  to  Sodium.  But 
besides  these  there  are  a  number  of  dark  lines  in  the 
solar  spectrum  which  do  not  correspond  to  any  known 
I  terrestrial  element.  In  addition  to  the  lines  of  Fraun- 
hofer, indubitably  belonging  to  the  sun,  there  are  many 
other  dark  lines  in  the  solar  spectrum  which  originate 
from  the  absorptive  action  of  the  terrestrial  atmo- 
sphere, and  are  therefore  called  atmospheric  lines.  That 
they  are  really  produced  by  the  atmosphere  is  easily 
recognised  by  the  fact  that  they  are  seen  more  distinctly 
or  even  first  make  their  appearance  when  the  sun  ap- 
proaches the  horizon,  and  when  consequently  its  rays 
have  to  traverse  a  much  greater  extent  of  the  terres- 
trial atmosphere.  The  Fraunhofer 's  lines  A  and  B, 
the  darkness  of  which  essentially  depends  on  the 
FIG.  118.  relative  position  of  the  sun,  mast 

on    this   account  be    regarded   as 
atmospheric. 

To  make  a  comparison  of  the 
spectra  of  metals  with  that  of  the 
sun  with  the  precision  required  for 
this  kind  of  investigation,  a  spectro- 
scope with  only  one  prism  is,  on  ac- 
count of  its  small  dispersive  power, 

Telescopes  with  four  prisms.         insufficient-  Kirchhoff,         there- 

fore, in  order  to  obtain  an  exact  drawing  of  the  solar 
spectrum  to  compare  with  the  lines  of  metallic  elements 
employed  a  spectroscope  with  four  prisms,  appropri- 
ately arranged  behind  one  another  (fig.  118),  together 
with  a  highly  magnifying  telescope.  By  this  instru- 


SPECTRUM   ANALYSIS   OF  THE  SUN.  1 67 

merit  fresh  lines  are  rendered  visible,  and  groups  of  lines, 
which  in  weaker  instruments  appear  only  as  misty  striee, 
are  resolved  into  their  several  lines.  Thus,  for  example, 
the  dark  line  D  can  be  shown  by  its  means  to  be  com- 
posed of  two  fine  lines,  D}  and  D2,  as  was  already  known 
to  Fraunhofer ;  and  in  the  same  way  the  bright  line  of 
Sodium  splits  into  two  lines  which  correspond  in  the 
most  precise  manner  with  two  solar  lines.  The  excel- 
lent drawings  of  the  solar  spectrum  made  by  Kirchhofi 

O 

and  Hoffman,  and  subsequently  by  Angstrom  and 
Thalen,  are  as  important  and  indispensable  for  the 
spectrum  analysis  of  the  sun  and  celestial  bodies  as  the 
chart  of  stars  is  to  the  astronomer  for  enquiry  into  the 
position  of  the  fixed  stars. 

73.  If  the  explanation  of  the  lines  of  Fraunhofer 
given  by  Kirchhoff  be  correct,  those  parts  of  the  solar 
atmosphere  which  project  at  the  edge  of  the  sun  beyond 
the  photosphere  should  exhibit  bright  lines  in  the 
spectroscope  in  place  of  the  dark  Fraunhofer's  lines. 

The  so-called  protuberances  afforded  an  instant  and 
crucial  test  of  the  truth  of  Kirchhoff's  hypothesis.  In 
total  eclipses  of  the  sun,  at  various  points  of  the  sun's 
edge  reddish  projections  appear,  which  sometimes  re- 
semble clouds,  sometimes  hook-like  curved  horns,  and 
sometimes  snowy  mountains  glowing  with  the  rosy 
tint  of  evening.  In  the  uneclipsed  sun  these  protu- 
berances cannot  be  seen,  because  their  feeble  light  is  lost 
in  the  brightness  of  the  terrestrial  atmosphere  during 
the  day.  The  first  spectrum  of  the  protuberances  was 
obtained  during  the  solar  eclipse  of  August  18,  1868. 
It  presented  bright  lines,  amongst  which  the  three  lines 
of  Hydrogen  (C,  jP,  and  one  a  little  in  front  of  6r),  and 
a  yellow  line  behind  the  double  line  D,  which  ccrre- 


1 68  OPTICS. 

spends  neither  to  a  Fraunhofer's  line,  nor  to  that  of 
any  known  terrestrial  substance,  and  which  has  been 
since  designated  D3,  are  the  most  conspicuous.  It  wap 
thus  demonstrated  that  the  protuberances  are  gaseous, 
and  that  they  are  principally  composed  of  hydrogen. 

Janssen,  who  was  sent  to  the  East  Indies  by  the 
French  Academy  of  Sciences  to  observe  this  eclipse, 
discovered  on  the  following  day  a  method  of  seeing  the 
bright  lines  of  the  protuberances  without  any  eclipse  of 
the  sun,  and  when  shining  at  its  brightest.  The  idea 
of  this  method  had  previously  been  suggested  by 
Lockyer,  and  had  been  carried  into  effect  by  him  before 
he  had  received  information  of  the  discovery  made  by 
the  French  observer. 

The  reason  that  we  are  unable  to  see  the  protu- 
berances with  an  ordinary  telescope  in  bright  sunshine 
is  on  account  of  the  great  brightness  of  the  terrestrial 
atmosphere,  rendered  luminous  by  the  sun,  which  over- 
powers the  feeble  light  of  the  protuberances.  In  order 
that  the  spectrum  of  the  protuberances  should  be  seen, 
it  is  necessary  to  lower  the  light  of  the  terrestrial  atmo- 
sphere to  a  sufficient  degree,  yet  without  at  the  same 
time  materially  weakening  that  of  the  protuberances. 

The  practicability  of  effecting  this  depends  on  the 
great  difference  that  exists  between  ordinary  daylight 
and  the  light  of  the  protuberances.  The  former  con- 
sists of  all  possible  kinds  of  rays,  and  gives,  apart  from 
Fraunhofer's  lines,  a  continuous  spectrum ;  the  latter, 
011  the  other  hand,  consists  of  only  a  few  homogeneous 
kinds  of  light,  to  which,  in  its  spectrum,  the  previously- 
mentioned  bright  lines  correspond.  By  multiplying 
the  prisms  of  the  spectroscope  the  continuous  spectrum 
of  ordinary  daylight  may  be  indefinitely  extended,  and 


SPECTRUM   ANALYSIS   OF  THE  SUN.  169 

Its  brilliancy  so  far  diminished  that  it  is  scarcely  to  be 
perceived.  By  the  same  system  of  prisms  the  bright 
lines  of  the  spectrum  of  the  protuberances  may  indeed 
be  separated  widely  from  one  another,  but  are  not  mate- 
rially weakened  in  brilliancy.  In  order,  therefore,  to 
see  them  distinctly  upon  the  dark  ground  of  the  almost 
imperceptible  spectrum  of  the  atmospheric  light,  it  is 
only  requisite  to  use  a  strongly  dispersing  spectroscope. 

Were  the  spectroscope  pointed  directly  towards  the 
sun,  light  from  all  its  parts  would  simultaneously  pene- 
trate the  slit  of  the  instrument  and  the  ordinary  solar 
spectrum  would  be  produced  ;  but  with  the  present  object 
in  view  it  is  necessary  that  each  segment  of  the  sun  should 
be  investigated  separately.  This  object  is  attained 
by  placing  a  spectroscope  instead  of  the  ocular  in  a 
telescope,  and  receiving  the  small  image  of  the  sun 
formed  at  the  focus  upon  the  plane  of  the  aperture  of 
the  slit.  By  this  means  any  given  part  of  the  sun's 
disk  or  edge  can  be  made  to  fall  separately  upon  the 
slit. 

This  arrangement  renders  it  possible  not  only  to 
recognise  by  its  bright  lines  the  presence  of  a  protube- 
rance, but  also  to  see  its  complete  form  with  well  defined 
borders.  If  we  make,  for  example,  the  slit  so  wide 
that  it  takes  in  the  whole  image  of  a  protuberance 
between  its  borders,  we  see  through  the  spectroscope  as 
many  images  of  it  as  there  are  homogeneous  rays  in 
the  light  of  the  protuberance.  These  images  are  quite 
sharply  defined,  and  in  consequence  of  the  great  dis- 
persion of  the  spectroscope,  are  so  widely  separated  from 
each  other  that  only  one  is  seen  in  the  field  of  vision, 
and  the  protuberance  can  be  seen  at  will,  red  by  virtue 
of  its  C  rays,  or  greenish  blue  by  its  F  rays.  This 


1 70  OPTICS. 

method  of  observation  cannot  be  applied  to  a  white 
object,  because  the  innumerable  coloured  images  would 
be  arranged  and  become  confused  in  a  continuous 
series.  The  protuberances  are  to  be  regarded  as 
violent  eruptions  of  gases,  which  are  shot  forth  to  an 
extraordinary  height  above  the  proper  solar  atmosphere 
(chromosphere)  and  it  is  to  their  absorptive  power  that 
the  Fraunhofer's  lines  are  due.  In  the  eclipse  of 
December  22,  1870,  the  American  observer  Young  also 
perceived  the  bright  lines  of  the  chromosphere  itself. 
He  made  the  following  report  upon  this  important  ob- 
servation, which  powerfully  supports  Kirchoff's  view  : 
'  As  the  solar  sickle  became  narrower,  I  remarked 
how  all  the  dark  lines  became  progressively  fainter, 
hut  I  was  wholly  unprepared  for  the  extraordinary 
phenomenon  which  in  an  instant  presented  itself  to  my 
eye  at  the  moment  when  the  dark  disk  of  the  moon  en- 
tirely covered  the  photosphere  of  the  sun.  The  whole 
field  of  vision  was  filled  with  bright  lines  which  suddenly 
appeared  with  the  greatest  brilliancy  and  then  again 
vanished,  so  that  after  the  lapse  of  scarcely  two  seconds 
nothing  remained  of  those  lines  which  had  just  been  the 
object  of  my  investigation.  It  is  obviously  impossible 
for  me  to  state  with  certainty  that  all  the  bright  lines 
which  filled  the  field  of  vision  occupied  exactly  the 
same  position  as  the  lines  of  Fraunhofer,  but  I  am  con- 
vinced that  it  was  so,  for  I  recognised  various  groups  of 
lines,  and  the  whole  disposition,  as  well  as  the  relative 
intensity  of  the  spectrum,  seemed  quite  familiar  to  me.' 
Since  this  observation,  which  was  made  during  an 
sclipse,  the  bright  lines  of  the  chromosphere  have  been 
seen  in  bright  sunshine  by  means  of  the  same  method 
of  research  as  that  above  detailed  for  examining  the 


SPECTRUM  ANALYSIS   OF  THE  SUN.  171 

protuberances.  Young  has  in  this  way  observed  not 
less  than  273  bright  lines  in  the  chromosphere,  oi 
which  64  belong  to  Iron. 

Spectrum  analysis  has  been  applied  with  the  greatest 
success,  not  to  the  sun  alone  but  to  other  celestial 
objects.  It  is  impossible,  however,  to  go  into  farthei 
detail  in  regard  to  the  results  obtained,  since  this  sub- 
ject is  beyond  the  limits  assigned  to  this  work. 


1 72  OPTICS, 


CHAPTER  XII. 

ABSOEPTION. 

74.  THAT  gaseous  bodies  are  capable  of  producing 
absorption  lines  not  only  in  the  incandescent  condition, 
but  at  far  lower  temperatures,  is  shown  by  the  above- 
mentioned  atmospheric  lines  of  the  solar  spectrum, 
which  are  essentially  due  to  the  aqueous  vapour  con- 
tained in  the  air.  Other  gases  possess  a  similar  power 
of  absorption,  two  examples  of  which  may  here  be 
mentioned. 

After  the  spectrum  of  the  electric  light  has  been 
thrown  upon  the  screen,  a  small  test-tube,  containing 
some  nitric  acid  and  copper,  is  placed  in  front  of  the 
slit.  As  the  acid  dissolves  the  metal,  a  yellowish-red 
gas  is  developed,  through  which  the.  rays  of  light  must 
pass  before  they  reach  the  prism. 

It  may  now  be  seen  (fig.  1 19,  1)  that  the  previously 
continuous  spectrum  is  interrupted  by  innumerable 
dark  lines  (Brewster  has  counted  about  2,000),  which 
closely  resemble  the  lines  of  Fraunhofer.  They  are 
sparingly  present  in  the  red  part,  but  are  more  closely 
arranged  towards  the  violet  end,  and  render  it  quite 
faint. 

If  a  little  Iodine  be  volatilised  in  another  test- 
tube,  arid  the  light  of  the  electric  lamp  be  transmitted 
through  the  beautiful  violet  vapour,  the  spectrum  maj 


ABSOKPTION. 


173 


again  be  observed  to  present  a  number  of  dark  lines 
(tig.  119,  2),  which,  however,  have  a  very  different 
arrangement  from  the  above.  They  are  principally 
situated  in  the  orange,  yellow,  and  green  ;  and  indeed 


FIG.  119. 


Absorption  spectra  of  nitrous  oxide  and  of  the  vapour  of  iodine. 

are  so  closely  grouped  in  the  latter  that  they  quite 
darken  it.  On  the  other  hand,  the  blue  and  violet  part 
of  the  spectrum  is  quite  free  from  them.  This  absorp- 
tion spectrum,  as  Wiillner  has  shown,  is  exactly  the 
converse  of  the  spectrum  of  glowing  Iodine  vapour. 
If,  for  example,  the  reddish-yellow  light  of  a  hydrogen 
flame,  saturated  with  Iodine  vapour,  be  examined 
through  the  spectrum  apparatus,  bright  lines  are  ob- 
tained at  those  points  where  the  absorption  spectrum 
appears  dark. 

The  reddish-yellow  colour  of  the  nitrous  acid,  and 
the  violet  colour  of  the  vapour  of  iodine,  are  the  neces- 
sary consequences  of  their  peculiar  powers  of  absorption ; 
for  as  the  nitrous  acid  arrests  certain  kinds  of  rays  of 
the  white  light  traversing  it,  and  especially  the  violet 
ones,  the  mixture  of  the  rest  is  no  longer  white,  but 
just  the  reddish-yellow  tone  of  colour  proper  to  this 
gas.  For  the  same  reason  Iodine  vapour,  being  almost 
opaque  for  the  yellow  and  green  rays,  exhibits  a  mixed 


1 74  OPTICS. 

tint,  formed  by  the  red,  blue,  and  violet  rays  which  it 
transmits,  and  which  appear  violet  to  our  eyes. 

75.  The  different  colours  of  transparent  solid  and 
fluid  bodies  similarly  result  from  their  peculiar  capa- 
bilities of  absorption,  a  series  of  examples  of  which  may 
now  be  given.  When  a  solution  of  permanganate  of 
potash  contained  in  a  glass  trough  with  parallel  walls 
is  placed  in  front  of  the  slit  of  the  Heliostat,*  (fig. 
120),  the  red  and  blue-violet  regions  of  the  spectrum 
appear  unaltered,  whilst  the  yellow  and  the  green 
appear  darkened,  and  upon  the  dark  ground  are  fine 
black  striae.  It  is  unnecessary  that  any  explanation 
should  here  be  entered  into  of  the  mode  in  which  the 
reddish-violet  colour  of  the  fluid  results  from  this 
phenomenon  of  absorption. 

If  again  blood  diluted  with  water  be  placed  in  the 
glass  trough,  the  violet  end  of  the  spectrum  vanishes, 
and  between  Dand  E  two  broad  dark  bands  (fig.  120,  2) 
make  their  appearance.  The  red  colour  of  blood  is 
thus  not  a  simple  colour,  but  a  mixture  of  all  those 
colours  which  still  remain  over  in  its  spectrum.  The 
slightest  chemical  alteration  in  blood  betrays  itself 
immediately  by  a  corresponding  change  in  the  spectrum. 
Thus  poisoning  by  carbonic  oxide  gas  (fire-damp),  or  by 
hydrocyanic  acid,  may  be  immediately  recognised  by 
the  changed  appearance  of  the  blood  spectrum.  The 
spectroscope  may  thus  render  important  services  to 
Physiology  and  Forensic  Medicine. 

Plants  owe  their  green  colour  to  the  'chlorophyll' 

*  If  these  exper.ments  are  made  with  the  light  of  the  sun,  the  Fraun- 
hofer's  lines  are  seen  in  addition  to  the  absorption  phenomenon  and  furnish 
satisfactory  points  of  comparison  for  the  determination  of  the  position  of 
the  absorption  lines 


ABSORPTION. 


175 


contained  in  their  cells.  An  alkaline  solution  of  this 
colouring  material  gives  a  highly  characteristic  spectrum 
(fig.  120,  3).  In  the  middle  of  the  red  is  a  deep  black 
band,  which  occupies  the  interspace  between  the  lines 


FIG.  120. 


Absorption  spectra. 

B  and  0;  three  feeble  absorption  striae  are  seen  in  the 
orange-yellow  and  green  ;  the  indigo-violet  part  of  the 
spectrum  from  F  onwards  is  completely  absent. 

If  a  piece  of  glass  coloured  blue  with  Cobalt  be  held 
in  front  of  the  prism,  the  spectrum  shown  in  fig.  120,  4, 
13 


176  OPTICS 

is  obtained.  In  this  the  whole  tract  from  B  to  F  is 
shaded,  with  the  exception  of  a  feebly  luminous  line 
in  the  yellow-green.  The  extreme  red,  on  the  other 
hand,  before  B,  as  well  as  the  entire  indigo-violet  extre- 
mity of  the  spectrum,  remains  uncha-nged. 

A  glass  coloured  red  with  oxide  of  Copper  gives  aii 
absorption  spectrum  of  a  far  more  simple  kind  than 
any  of  those  hitherto  mentioned  (fig.  120,  5).  This  kind 
of  glass  only  allows  the  red  and  orange-red  rajs  as  far 
as  D  to  pass  through  it;  it  is  quite  opaque  for  all 
other  colours.  If  a  red  glass  be  placed  before  a  blue 
cobalt  glass  the  combination  produces  by  absorptive 
action  a  nearly  homogeneous  light,  namely,  the 
extreme  dark  red  in  front  of  B,  which  is  the  only 
colour  that  the  two  glasses  are  together  capable  of 
transmitting. 

A  solution  of  Potassium  bichromate  is  only  trans- 
parent for  the  less  refrangible  part  of  the  spectrum  as 
tar  as  to  the  Fraunhofer's  line  b  (fig.  120,  6).  A  solu- 
tion of  the  ammoniated  oxide  of  Copper  is  transparent 
only  for  the  more  refrangible  part,  from  about  the  line 
6  onwards  (fig.  120,  7).  The  orange-yellow  colour  of 
the  first-named  solution,  and  the  blue  of  the  second, 
are  consequently  complementary  to  each  other.  Two 
glass  cells  filled  with  these  fluids,  and  placed  one  be- 
hind the  other,  scarcely  permit  the  passage  of  any  light. 
The  one  fluid  looked  at  through  the  other  appears 
completely  black.  Nevertheless  absorption  does  not 
always  produce  the  particular  tone  of  the  transmitted 
light.  If  only  a  very  small  extent  of  the  spectrum  be 
absorbed,  the  mixture  of  the  transmitted  rays  does  not 
differ  remarkably  from  white.  As  an  example  of  this, 
ft  piece  of  glass  may  be  adduced  which  contains  in  a 


ABSORPTION.  177 

state  of  chemical  combination  the  rare  metal  Didy- 
miuiD.  To  the  naked  eye  it  appears  nearly  colourless, 
but  if  it  be  brought  in  front  of  the  slit,  two  thin  black 
striae  appear  in  the  spectrum  at  the  line  D,  and  two  less 
well-marked  ones  in  the  green  at  E  and  b  (fig.  120,  8), 
which  are  so  characteristic  of  Didymium  that  they  enable 
the  smallest  quantity  of  this  metai  in  solution  to  be 
detected.  If  the  solid  oxide  of  Didymium  be  heated  to 
incandescence,  bright  lines  appear  in  the  spectrum  of  the 
emitted  light  in  place  of  the  dark  lines.  We  have  thuj 
in  Didymium  an  example  of  a  solid  which  when  in- 
candescent does  not  give  a  continuous  but  a  linear 
spectrum.  The  oxides  of  the  metals  Erbium  and  Ter 
biuin,  which  are  also  rare,  behave  in  a  similar  manner. 
If  an  absorbing  substance  be  employed  in  a  pro  • 
gressively  thicker  layer  or  in  a  greater  degree  of  concen- 
tration, the  absorption  bands  become,  without  changing 
their  position,  broader  and  darker,  and  colours  which 
were  previously  transmitted  gradually  disappear.  Thus* 
it  comes  to  pass  that  with  increasing  thickness  or  con- 
centration the  tone  of  colour  of  the  transmitted  light 
frequently  becomes  quite  different.  To  demonstrate 
this  a  number  of  gelatine  disks  coloured  with  litmus 
may  be  used,  which  are  placed  between  two  colourless 
glass  plates  in  a  graduated  manner.  If  these  be  placed 
before  the  slit,  there  will  be  seen  in  the  spectrum 
(fig.  121)  the  graduated  amount  of  absorption  corre- 
sponding to  the  different  thicknesses  of  the  gelatine.  In 
the  case  of  the  thinnest  layer  only  a  thin  dark  band  is 
seen  in  front  of  1),  whilst  the  thickest  laj^er  only  per- 
mits the  red  end  of  the  spectrum  to  be  seen.  The 
appearance  of  this  spectrum  explains  why  a  layer  of 
litmus  gradually  increasing*  in  thickness  first  appears 


178 


OPTICS. 


whitish,  then  blue,  then  violet,  and  finally  purple-red. 
Similarly  a  solution  of  chlorophyll,  which  in  a  thin 
layer  appears  green,  transmits  when  very  thick  only 
the  extreme  dark-red  rays. 


FIG.  121. 


Absorption  of  the  colouring  matter  of  litmus  with  different  thicknesses  of  the  layer. 

The  absorption  spectra  being  thus  not  less  charac- 
teristic in  demonstrating  the  presence  of  the  bodies  to 
which  they  belong  than  are  the  spectra  of  the  light 
emitted  from  glowing  vapours,  spectral  analysis  opens 
up  a  wide  field  of  application.  The  discovery  of  adul- 
teration of  colouring  matters  and  of  food  may  be  particu- 
larly mentioned  in  practical  life. 

76.  In  the  experiments  hitherto  made  the  rays 
emerging  from  the  prism  have  been  received  upon  a 
paper  screen  because  the  rough  surface  of  the  paper 
reflects*  the  different  coloured  rays  diffusely,  enabling 
the  complete  spectrum  to  be  seen  on  all  sides.  Instead 
of  the  usually  perfectly  white  screen,  another  one  may 
be  selected,  the  upper  half  of  which  is  covered  with 
white  and  the  lower  half  with  red  paper.  The  screen 
must  be  placed  in  such  a  position  that  the  horizontal 
line  of  junction  of  the  two  papers  halves  the  spectrum 
throughout  its  whole  length.  In  its  upper  half,  which 

*  See  §§  8  and  15. 


ABSOKPTION.  179 

falls  upon  the  white  paper,  the  spectrum  exhibits  all 
the  colours  as  clearly  as  before,  but  in  the  lower  half, 
which  falls  on  the  red  paper,  the  colours  yellow,  green, 
blue,  and  violet  are  almost  entirely  absent,  whilst  the 
red  and  orange  are  almost  as  bright  as  when  they  fall 
en  the  white  screen  (fig.  120,  9). 

This  experiment  proves  that  the  red  paper  possesses 
in  a  high  degree  the  power  of  reflecting  diffusely  the 
red  and  orange-coloured  rays,  but  that  it  does  not 
reflect  the  other  kinds  of  rays  falling  upon  it,  but,  on 
the  contrary,  swallows  them  up,  or,  as  we  say,  absorbs 
them.  It  is  obvious  therefore  why  this  paper  appears 
red  when  illuminated  by  the  white  light  of  day. 

If  this  experiment  be  repeated  with  yellow,  green, 
and  blue  paper  successively,  it  will  be  found  that  each 
absorbs  other  parts  of  the  spectrum,  and  that  the  par- 
ticular colour  which  it  possesses  in  daylight  is  always 
the  tint,  caused  by  mixture  of  all  those  rays  which  it 
diffusely  reflects. 

White  paper  absorbs  no  one  of  the  homogeneous 
colours  present  in  the  light  of  the  sun  in  particular,  but 
reflects  all  in  their  original  state  of  mixture,  and  ib  is 
on  this  account  that  it  appears  by  daylight  white.  A 
surface  is  called  grey  which  possesses  an  equally  small 
power  of  diffusion  for  all  colours.  Lastly,  everything 
appears  black  the  surface  of  which  is  of  such  a  nature 
that  all  kinds  of  rays  are  absorbed  by  it. 

The  whole  range  of  colours  presented  by  objects  in 
all  their  variety  may  thus  be  explained  on  the  principle 
of  absorption.  All  objects,  whether  seen  by  transmitted 
or  by  reflected  light,  exhibit  exactly  that  colour  which 
is  complementary  to  the  sum  of  the  rays  absorbed. 

The  bright  fresh  green  of  plants,  for  example,  re- 


1 80  OPTICS. 

suits  from  the  absorbing  action  of  chlorophyll,  and  has 
therefore  the  same  composition  as  the  light  passing 
through  a  solution  of  chlorophyll  (see  fig.  120,  3).  It 
contains,  namely,  the  extreme  red  in  front  of  the 
Fraunhofer's  line  B  quite  undiminished  in  intensity, 
the  orange-yellow  and  green  between  C  and  E  with 
tolerably  strong  brilliancy,  and  a  little  blue,  but  the 
middle  part  of  the  red  (corresponding  to  the  absorption 
striue  between  B  and  C)  as  well  as  the  indigo  and  violet 
from  the  middle  between  F  and  6r,  are  almost  com- 
pletely absent. 

This  peculiar  composition  of  the  green  colour 
of  plants  explains  the  surprising  appearance  which 
a  well-wooded  landscape  presents  on  a  sunny  day  if 
looked  at  through  two  properly  selected  glass  plates, 
of  which  one  is  a  blue  cobalt  glass  whilst  the  other 
is  faintly  tinted  with  oxide  of  copper.  Spectacles  made 
of  these  two  glasses  superimposed  on  one  another 
(erythrophytoscope)  permit  only  the  extreme  red  con- 
stituent of  the  green  colour  of  plants,  with  some  blue- 
green  and  blue  but  no  green  or  yellow,  to  reach  the 
eye.  The  foliage  of  plants  is  therefore  seen  coloured  of 
a  beautiful  red,  whilst  the  bright  sky  is  of  a  deep  violet- 
blue  colour,  the  clouds  of  a  delicate  purpJe,  and  the 
earth  and  rocks  of  a  violet- grey. 

77.  The  essential  nature  of  the  colours  of  objects 
may  thus  be  strikingly  indicated,  by  saying  that  they 
are  the  residue  of  the  light  by  which  they  are  illumi- 
nated after  abstraction  of  those  rays  which  are  extin- 
guished by  absorption.  It  follows  as  a  matter  of  course 
that  objects  can  only  exhibit  such  colours  in  transmitted 
as  well  as  in  diffusely  reflected  light  as  are  already  con- 
tained  in  the  incident  light.  Hence  in  order  that  a 


ABSOEPTION.  161 

sheet  of  red  paper  should  appear  red,  red  rays  must  be 
contained  in  the  light  by  which  it  is  illuminated.  The 
light  of  day  contains  such  rays.  But  if  the  room  be 
darkened  and  the  paper  illuminated  with  the  monochro- 
matic yellow  flame  of  Sodium,  it  a,ppears  black. 

With  homogeneous  illumination  differences  of  co- 
_our  are  no  longer  perceptible.  The  variations  of  light 
and  shade  are  alone  visible.  Hence  the  wreath  of 
flowers  which  appeared  so  luxuriant  in  the  above  expe- 
riment would,  when  seen  with  homogeneous  light,  seem 
withered  and  yellow ;  and  a  picture,  rich  as  it  might 
really  be  in  colour,  would  resemble  a  sepia  drawing. 
Were  the  sun  a  sphere  of  glowing  vapour  of  Sodium, 
all  terrestrial  nature  would  present  this  monotonous  and 
gloomy  aspect.  It  requires  the  white  light  of  the  sun,  in 
which  innumerable  colours  are  blended,  to  disclose  to 
our  eyes  the  variegated  tints  of  natural  objects.  And 
so  again,  if  a  Magnesium  wire  be  held  in  the  Sodium 
flame,  its  white  light,  as  by  a  stroke  of  magic,  restores 
the  fresh  colours  to  the  wreath  of  flowers,  to  the  pic- 
ture, and  everything  around. 

The  light  of  gas  and  candles  contains  all  the  colours 
of  the  solar  spectrum,  though  not  mixed  in  exactly  the 
same  proportion.  The  yellow  rays  are  very  abundant, 
whilst  the  blue  and  violet  are  relatively  much  less 
abundant  than  in  solar  light.  This  affords  an  explana- 
tion of  the  well-known  fact  that  green  and  blue  clothing 
materials  are  difficult  to  distinguish  by  candlelight. 
For  green  materials  reflect  especially  the  green  and  a 
few  blue  rays ;  blue  materials,  in  addition  to  the  green, 
the  blue  rays  especially  ;  but  since  blue  is  only  sparingly 
present  in  candlelight,  whilst  green  is  abundant, 


182  OPTICS. 

objects   presenting    both    colours   by   daylight   appear 
more  or  less  of  a  green  colour  by  candlelight. 

If  the  two  colours  are  mingled  the  mixture  presents 
that  colour  which  remains  over  after  the  abstraction  of 
all  the  rays  absorbed  by  the  two  materials.  It  is,  for 
example,  generally  known  that  a  mixture  of  blue  and 
yellow,  as  of  Prussian  blue  and  gamboge,  produces  a 
green.  This  is  by  no  means  in  opposition  to  the  fact 
above  stated  (§  57),  that  the  yellow  and  the  blue  of 
the  spectrum  unite  to  form  white.  For  in  order  that 
our  eyes  should  receive  the  impression  of  white  it  is 
necessary  that  blue  and  yellow  rays  should  enter  them 
simultaneously.  A  mixture  of  Prussian  blue  and  gam- 
boge emits  neither  blue  nor  yellow,  but  essentially 
green  rays.  The  former  colouring  matter  absorbs  the 
red  and  yellow,  the  latter  the  blue  and  violet  rays,  and 
the  green  rays  therefore  alone  remain  in  the  diffuse 
light  reflected  from  the  mixture. 


FLUORESCENCE.  183 


CHAPTER  XIII. 

FLUORESCENCE.      PHOSPHORESCENCE.       CHEMICAL  ACTION. 

78.  THE  question  now  arises,  what  becomes  of  the 
rays  that  have  undergone  absorption  ?  Are  they  in 
fact,  as  they  appear  to  be,  annihilated?  A  series  of 
phenomena  now  to  be  considered  will  give  us  an  answer 
to  these  questions. 

If  water  containing  a  little  ^Esculin,  a  substance  con- 
tained in  the  bark  of  the  horse  chestnut  in  solution,  be 
placed  in  a  flask,  and  the  rays  FlG  122 

of  the  sun  or  of  the  electric  lamp 
concentrated  by  a  lens  situated 
at  aboutits  focal  distance  from 
the  vessel,  be  directed  upon  it, 
the  cone  of  light  thrown  by 
the  lens  into  the  interior  of  the 
fluid  will  be  seen  to  shine  with  Fluorescence. 

a  lovely  sky-blue  tint.  The  particles  of  the  solution  of 
jJEsculin  in  the  path  of  the  beam  become  spontane- 
ously luminous,  and  emit  a  soft  blue  light  in  all  direc- 
tions. The  cone  of  light  appears  brightest  at  the  point 
where  it  enters  into  the  fluid  through  the  glass,  and 
quickly  diminishes  in  brilliancy  as  it  penetrates  more 
deeply. 

There  are  great  numbers  of  fluid  and  solid  bodies 


134  OPTICS. 

which  become  similarly  self-luminous  under  the  in- 
I  fluence  of  light.  This  peculiarity  was  first  observed  in 
a  kind  of  spar  occurring  at  Alston  Moor  in  England, 
which,  itself  of  a  clear  green  colour,  appears  by  trans- 
mitted solar  light  of  a  very  beautiful  indigo-violet 
colour.  From  its  occurrence  in  Calcium  fluoride  the 
phenomenon  has  been  named  fluorescence. 

In  order  to  understand  more  precisely  the  circum- 
stances under  which  fluorescence  occurs,  the  solution  of 
JEsculin  must  again  be  referred  to.  The  light  before 
it  reaches  the  lens  must  be  allowed  to  pass  through 
just  such  another  solution  of  .ZEsculin  contained  in  a 
glass  cell  with  parallel  walls.  The  cone  of  light  pro- 
ceeding from  the  lens,  as  long  as  it  passes  through  the 
air,  does  not  appear  to  have  undergone  any  material 
change,  it  is  just  as  bright  and  just  as  white  as  before. 
In  the  interior  of  the  fluid  however  it  no  longer  presents 
a  blue  shimmer  but  becomes  scarcely  perceptible. 

Thus  it  is  seen  that  light  which  has  traversed  a 
solution  of  .ZEsculin  is  no  longer  capable  of  exciting 
fluorescence  in  another  solution  of  jEsculin.  Those  rays 
consequently  which  possess  this  property  mast-  be 
arrested  by  the  first  solution  of  -ZEsculin.  Similar 
results  are  obtained  in  the  case  of  every  other  fluores- 
cent substance. 

The  general  proposition  can  therefore  be  laid  down, 
thai  a  body  capable  of  exhibiting  fluorescence  fluoresces  by 
virtue  of  those  rays  which  it  absorbs. 

In  order  to  determine  what  rays  in  particular  cause 
the  fluorescence  of  JDsculin,  the  spectrum  must  be  pro- 
jected in  the  usual  way ;  but  instead  of  its  being 
received  upon  a  paper  screen  it  must  be  allowed  to  fall 
upon  the  wall  of  a  glass  cell  containing  a  solution  of 


FLUORESCENCE.  185 

JEsculin,  that  is  to  say,  upon  the  solution  itself,  and  it 
must  then  be  observed  in  what  parts  of  the  spectrum 
the  blue  shimmer  appears.     The  red  and  all  the  other 
colours    consecutively   down   to   indigo 
appear  to  be  absolutely  without  effect. 
The  bluish  shimmer  first  commences  in 
the  neighbourhood  of  the  line   G,  and 
covers   not  only  the  violet  part  of  the 
spectrum,    but  stretches  far   beyond  the 
group  of  lines  H  to  a  distance  which  is 
about  equal  to  the  length  of  the  spec- 
trum   visible   under    ordinary   circum-    IS        M 
stances.  5 

From  this  the  conclusion  must  be 
drawn  that  there   are   rays  which  are    H  I    J 

still  more  refrangible  than  the  violet, 
but  which  in  the  ordinary  mode  of  pro- 
jecting the  spectrum  are  invisible ;  these 
are  termed  the  ultra-violet  rays.  They 
become  apparent  in  the  -ZEsculin  solu- 
tion because  they  are  capable  of  exciting 
the  bluish  fluorescent  shimmer  in  it.  • 
If  sunlight  have  been  used  in  the  above 
experiments  the  well-known  Fraun- 
hofer's  lines  appear  upon  the  bluish 
ground  of  the  fluorescing  spectrum,  not 
only  from  G  to  H,  but  the  ultra-violet 
part  also  appears  filled  with  numerous 
lines,  the  most  conspicuous  of  which  are 
indicated  by  the  several  letters  L  to  8 
(fig.  123).  That  these  lines,  like  the  ordinary  Fraun- 
hofer's  lines,  belong  properly  to  solar  light,  and  do  not 
depend  upon  any  action  of  the  fluorescing  substance,  is 


186  OPTICS. 

evident  from  the  circumstance  that  with  the  electric 
light  they  are  no  more  apparent  in  the  ultra-violet 
than  in  the  other  colours,  and  further,  because  the 
same  lines  are  seen  in  the  solar  spectrum,  whatever  may 
be  the  fluorescing  substance  under  examination. 

Quartz  has  the  power  of  transmitting  the  ultra- 
violet rays  far  more  completely  than  glass.  If  there- 
fore the  glass  lens  and  prism  hitherto  used  for  project- 
ing the  spectrum  be  replaced  by  a  quartz  lens  and 
prism,  the  ultra-violet  part  of  the  spectrum  is  rendered 
much  brighter  and  is  extended  still  further  than 
before. 

The  ultra-violet  rays  of  the  spectrum  can,  more- 
over, be  seen  without  the  intervention  of  any  fluorescing 
substance  through  a  glass,  or  still  better,  through 
a  quartz  prism,  if  the  bright  part  of  the  spectrum 
between  B  arid  H  be  carefully  shut  off.  With  feeble 
illumination  its  colour  appears  indigo-blue,  but  with 
light  of  greater  intensity  it  is  of  a  bluish-grey  tint 
(lavender).  The  ultra-violet  rays  thus  ordinarily  escape 
observation,  because  they  produce  a  much  feebler  im- 
pression on  the  human  eye  than  the  less  refrangible 
rays  between  B  and  H. 

An  explanation  is  thus  afforded  why  the  solution  of 
^Esculin,  apart  from  its  absorption,  is  colourless  when 
seen  by  transmitted  light;  for  since  it  absorbs  only 
the  feebly  luminous  violet  and  the  entirely  imperceptible 
ultra-violet  rays,  the  mixed  light  that  has  passed 
through  it  still  appears  white  and  is  not  rendered 
materially  fainter. 

79.  If  the  solar  spectrum  be  thrown  in  the  above- 
mentioned  manner  upon  the  fluid,  its  fluorescing  part 
everywhere  exhibits  the  same  bluish  shimmer;  and  spec- 


FLUORESCENCE.  187 

troscopic  examination  shows  that  this  bluish  light  has 
always  the  same  composition,  whether  it  is  excited  by 
the  G  rays  or  by  the  H  rays  or  by  the  ultra-violet  rays, 
and  that  it  is  formed  of  a  mixture  of  red,  orange,  yellow, 
green,  and  blue.  It  is  thus  seen  that  the  different 
kinds  of  homogeneous  light,  as  far  as  they  are  generally 
effective,  produce  compound  fluorescent  light  of  identi- 
cal composition,  the  constituents  of  which  neverthe- 
less are  collectively  less  refrangible  than,  or  are  at  most 
equally  refrangible  with,  the  exciting  rays. 

Amongst  other  fluorescing  bodies  may  be  mentioned 
the  solution  of  Quinine,  which  is  as  clear  as  water,  and 
has  a  bright  blue  fluorescence;  the  slightly  yellow 
Petroleum,  with  blue  fluorescence  ;  the  yellow  solution 
of  Turmeric,  with  green  ;  and  the  bright  yellow  glass 
containing  Uranium,  which  fluoresces  with  beautiful 
bright  green  fluorescence.  It  admits  of  easy  demonstra- 
tion that  in  these  bodies  also  it  is  the  more  refrangible 
rays  that  call  forth  fluorescence.  For  if  we  illuminate 
them  with  light  which  has  passed  through  a  red  glass 
no  trace  of  fluorescence  is  visible.  But  if  the  red  be  ex- 
changed for  a  blue  glass  the  fluorescence  becomes  as 
strongly  marked  as  with  the  direct  solar  light.  A  re- 
markable phenomenon  is  presented  in  the  splendid 
bright  green  light  which  is  emitted  by  Uranium  glass 
under  the  action  of  blue  illumination. 

The  highly  refrangible  rays  which  possess  in  so  high 
a  degree  the  power  of  exciting  fluorescence  are  con- 
tained in  large  proportion  in  the  light  emitted  by  a 
Geissler's  tube  (see  §  68)  filled  with  rarefied  nitrogen. 
In  order  to  expose  fluorescing  fluids  to  the  influence 
of  this  light  the  arrangement  represented  in  fig.  124 
may  be  employed  with  advantage.  A  narrow  tube 


188 


OPTICS. 


is  surrounded  by  a  wider  glass  tube,  into  which  the 
fluid  is  introduced  by  a  side  opening  which  can  be 
closed  if  required.  Another  form  of  Geissler's  tube  is 
represented  in  fig.  125,  which  contains  in  its  interior  a 


PIG.  125. 


FIG.  124. 


Geissler's  fluorescence  tube. 


Geissler's  tube  with  Uranium  glass  spheres. 


number  of  hollow  spheres  composed  of  Uranium  glass. 
Where  a  beam  of  the  reddish  violet  nitrogen  light  tra- 
verses the  tube  the  Uranium  glass  balls  shine  with  a 
beautiful  bright  green  fluorescent  light. 

The  electric  light  passing  between  carbon  points  is 
rich  in  rays  of  high  refrangibility,  indeed  the  ultra- 
violet end  of  its  spectrum  reaches  even  further  than  that 


FLUORESCENCE.  189 

of  the  solar  spectrum.  In  the  light  of  the  Magnesium 
lamp  the  ultra-violet  rays  are  also  abundant,  and  both 
sources  of  light  are  therefore  particularly  well  adapted 
to  produce  fluorescence,  whilst  gas  and  candlelight  are 
nearly  inoperative  on  account  of  the  small  amount  of 
the  more  refrangible  rays  they  contain. 

80.  It  would  nevertheless  be  incorrect  to  infer 
from  the  above  facts  that  the  more  refrangible  rays  are 
exclusively  capable  of  exciting  fluorescence.  A  red 
fluid  which  is  an  alcoholic  solution  of  Naphthalin  red 
(Rose  de  Magdala,  an  anilin  colouring  material)  and 
which  even  in  ordinary  daylight  fluoresces  with  orange 
yellow  tints  of  unusual  brilliancy,  will  serve  to  demon- 
strate that  even  the  less  refrangible  rays  are  capable 
of  producing  this  effect.  In  fact,  if  Ihe  spectrum  be  pro- 
jected upon  the  glass  cell  containing  the  fluid  (fig.  126,  2), 
the  yellow  fluorescent  light  will  be  seen  to  commence  at 
a  point  intermediate  to  C  and  D,  and  therefore  still  in 
the  red,  and  to  extend  over  the  whole  remaining  spec- 
trum as  far  as  to  the  ultra-violet.  The  strongest  fluo- 
rescence by  far  is  shown  behind  the  line  D  in  the 
greenish-yellow  rays.  It  then  again  diminishes,  and 
becomes  a  second  time  more  marked  between  E  and  6, 
from  thence  onward  the  fluorescence  becomes  fainter, 
then  increases  again  in  the  violet,  and  gradually 
vanishes  in  the  ultra-violet.  In  Naphthalin  red,  there- 
fore, there  are  rays  of  low  refrangibility,  namely,  the 
green-yellow  rays  behind  D,  by  which  its  fluorescence  is 
most  powerfully  excited. 

The  fluorescing  spectrum  received  upon  the  fluid 
shows,  as  we  have  already  mentioned,  three  regions  of 
stronger  fluorescence,  and  the  absorption  spectrum  of 
Naphthalin,  which  by  placing  a  small  cell  filled  with  the 


190  OPTICS. 


solution  in  front  of  the  slit  may  be  obtained  upon  a  paper 
screen,  gives  a  key  to  the  cause  of  this  phenomenon. 
In  this  spectrum  (fig.  126, 1)  a  completely  black  band  is 
visible  in  the  green-yellow  behind  D,  a  dark  band 


FIG. 126. 


Absorption  and  fluoresctng  spectrum  of  Naphthalin  red. 

between  E  and  6,  whilst  the  violet  end  appears  shaded. 
On  employing  a  very  strong  solution  of  the  Naph- 
thalin colouring  material,  the  whole  spectrum  vanishes 
with  the  exception  of  the  red  end,  which  remains  ap- 
parent to  a  point  behind  G.  If  now  the  absorption 
spectrum  be  compared  with  that  thrown  upon  the  fluid, 
the  intimate  relation  between  absorption  and  fluo- 
rescence that  has  already  been  pointed  out  in  the  -ZEscu- 
lin  solution  is  corroborated  in  the  minutest  particulars. 
For  every  dark  band  in  the  absorption  spectrum  corre- 
sponds to  a  bright  band  in  the  fluorescing  spectrum.  Every 
ray  absorbed  by  the  fluid  occasions  fluorescence,  and  the 
fluorescent  light  produced  by  it  is  the  brighter  the  more 
completely  the  ray  is  absorbed. 

A  second  example  of  the  excitation  of  fluorescence 
by  rays  of  small  refrangibility  is  exhibited  by  a  solu- 
tion of  chlorophyll.  The  spectrum  projected  upon  this 
green  fluid  fluoresces  of  a  dark  red  colour,  from  B  to  a 
point  within  the  ultra-violet,  exhibiting  at  the  same  time 


PHOSPHORESCENCE.  191 

bright  bands  which  correspond  with  the  dark  bands  in 
the  absorption  spectrum  (fig.  120,  3).  Between  B and  C, 
where  the  greatest  amount  of  absorption  occurs,  the 
fluorescence  is  also  the  most  marked.  But  it  is  the 
middle  red  rays  which  here  act  most  powerfully  as 
excitants.  It  is  remarkable  that  the  red  fluorescent 
light  which  the  chlorophyll  solution  emits  likewise  lies, 
in  regard  to  its  refrangibility,  between  B  and  G.  Ohio- 
rophyll  solution  affords  a  proof  that  all  rays  of  jbhe 
spectrum,  with  the  exception  of  the  extreme  red  in 
front  of  By  are  capable  of  calling  forth  fluorescence. 
Their  capacity  for*  doing  so  depends  simply  on  the 
power  of  absorption  of  the  fluorescing  substance.  The 
most  refrangible  violet  and  ultra-violet  rays  are,  how- 
ever, cnaracterised  by  the  circumstance  that  they  are 
capable  of  exciting  all  known  fluorescing  bodies. 

81.  Fluorescent  light  is  only  perceived  so  long  as 
the  fluorescent  substance  is  illuminated  by  the  exciting 
ravs.  As  soon  as  the  light  falling  on  it  is  obstructed 
the  coloured  shimmer  vanishes.  It  is  only  in  the  case 
of  some  fluorescing  solid  substances,  as  for  example, 
Fluor-spar  and  Uranium  glass,  that,  with  the  aid  of  ap- 
propriate apparatus  (Becquerel's  Phosphoriscope),  a  very 
short  continuance  of  the  fluorescence  may  be  observed 
to  take  place  in  the  dark. 

There  are,  however,  a  number  of  bodies  which,  after 
being  excited  to  self-luminosity  by  a  brilliant  light, 
continue  to  shine  for  a  certain  time  in  the  dark.  A 
series  of  pulverulent  white  substances,  namely,  the 
sulphur  compounds  of  Calcium,  Strontium,  and  Barium 
(which  should  be  kept  in  hermetically  sealed  glass  tubes), 
do  not  exhibit  the  faintest  light  in  a  dark  room. 
Moreover,  if  they  be  covered  with  a  yellow  glass  and 
14 


L92  OPTICS. 

illuminated  with  the  light  of  a  Magnesium  lamp,  they 
remain  as  dark  as  before.  But  if  the  yellow  be  ex- 
changed for  a  blue  glass,  and  the  Magnesium  light  be 
allowed  to  play  upon  them  for  a  few  seconds  only,  they 
emit  in  the  dark  a  soft  light,  each  powder  having  its 
own  proper  tint  of  colour.  This  power  of  shining  in 
the  dark  after  having  been  exposed  to  light  is  termed 
phosphorescence.  *  The  property  is  possessed  in  a  high 
degree  not  only  by  the  above-named  artificially  pre- 
pared substances,  but  by  various  minerals,  as  the  dia- 
mond, fluor-spar,  and  a  variety  of  fluor-spar  called 
Chlorophane. 

Phosphorescence,  like  fluorescence,  is  an  effect  of 
absorbed  light.  For  the  refrangible  rays  which,  in 
accordance  with  the  results  of  the  experiments  that 
have  been  made,  are  alone  capable  of  exciting  these 
substances  to  self-luminosity  are  exactly  those  which 
they  absorb.  Phosphorescent  light  itself,  examined 
spectroscopically,  is  found  to  be  composed  of  rays  the 
refrangibility  of  which  is  smaller  than  that  of  the  excit- 
ing rays,  and  it  is  indeed  compound  even  when  the 
exciting  light  is  homogeneous.  The  affinity  between 
phosphorescence  and  fluorescence  which  expresses  itself 
in  this  relation  is  unmistakable.  Phosphorescence  may 
be  described  as  fluorescence  which  is  prolonged  for  a 
certain  length  of  time  beyond  the  action  of  the  exciting 
rays. 

A  remarkable  fact  discovered  by  Becquerel  must  not 
here  be  passed  over  in  silence.  When  a  card  covered 
with  Strontium  sulphide  is  made  feebly  phosphorescent 
by  daylight,  and  a  solar  spectrum  is  then  projected  upon 
it  in  a  dark  chamber,  we  observe  in  the  course  of  a  few 
seconds  after  the  opening  in  the  shutter  has  been  closed 


PHOSPHORESCENCE.  193 

that  the  whole  surface  of  the  card  still  continues  to 
shine,  with  the  exception  of  that  part  on  which  the 
less  refrangible  portion  of  the  spectrum  from  A  to  F 
previously  fell.  In  that  part  no  phosphorescence  is 
visible.  The  less  refrangible  rays  are  thus  not  only 
incapable  of  exciting  phosphorescence,  but  they  appear 
even  to  destroy  or  disturb  the  phosphorescence  called  forth 
by  the  more  refrangible  rays. 

In  order  to  avoid  misunderstanding,  it  must  further 
be  remarked  that  the  light  of  phosphorus  (apart  from 
the  similarity  of  the  name),  the  light  of  touchwood,  of 
fire-flies,  of  various  marine  animals,  etc.,  does  not  belong 
to  the  class  of  phosphorescent  phenomena  caused  by 
the  absorption  of  light  which  we  have  here  considered. 
These  bodies  are  rather  to  be  regarded  as  self-lumi- 
nous in  consequence  of  chemical  and  physiological 
processes. 

82.  The  nature  of  the  substances  exhibiting  fluo- 
rescence or  phosphorescence  owing  to  the  rays  of  light 
they  have  absorbed  is  in  no  way  altered.  There  are, 
however,  a  number  of  bodies  which  undergo  a  perma- 
nent change  in  their  nature — an  alteration  of  their 
chemical  composition — from  exposure  to  light.  Every- 
one must  be  familiar  with  numerous  examples  of  this 
chemical  action  of  light  from  the  phenomena  of  daily 
life,  and  it  is  only  necessary  to  mention  such  cases  as 
the  bleaching  of  linen  and  of  wax,  the  fading  of  coloured 
stuffs,  and  the  blanching  of  water-colour  drawings. 

How  powerfully  the  chemical  action  of  light  can  be 
exerted  under  certain  circumstances  may  be  shown  by 
the  following  experiment.  A  mixture  of  equal  parts  oi 
Chlorine  and  Hydrogen  is  introduced  into  a  thin  glass 
ball.  If  this  be  exposed  to  the  daylight  the  two  gasea 


194  OPTICS. 

gradually  combine  to  form  Hydrochloric  acid  gas,  a 
chemical  compound  the  aqueous  solution  of  which  is 
generally  known  under  the  name  of  Muriatic  or  Hydro- 
chloric acid.  But  if  the  light  of  the  Magnesium  lamp 
be  allowed  to  fall  on  the  sphere  it  instantly  bursts  with 
a  loud  explosion,  and  is  broken  into  a  thousand 
fragments ;  that  is  to  say,  under  the  influence  of  this 
brilliant  light  the  chemical  combination  of  the  two  gases 
and  the  associated  development  of  heat  takes  place 
with  such  suddenness  that  the  thin  glass  is  unable  to 
resist  the  pressure  exerted. 

If  a  yellow  glass  be  placed  in  front  of  the  Magne- 
sium lamp,  and  the  yellow  light  transmitted,  which 
contains  only  the  less  refrangible  rays  of  the  spectrum, 
be  allowed  to  act  upon  another  of  these  little  glass  balls 
filled  with  the  same  mixture  of  gases,  the  ball  will  not 
explode,  but  it  bursts  directly  if  the  yellow  be  ex- 
changed for  a  blue  glass.  The  conclusion  therefore 
may  be  drawn  that  it  is  only  the  more  refrangible  rays 
of  the  spectrum  that  are  capable  of  inducing  the 
chemical  combination  of  Hydrogen  with  Chlorine. 

Whilst  in  the  example  just  given  the  rays  of  light 
induce  the  chemical  combination  of  two  elementary 
substances,  in  other  cases  they  can  effect  the  decomposi- 
tion of  compound  bodies.  This  is  pre-eminently  the 
case  with  the  salts  of  silver  on  which  Photography 
depends.  The  photographic  process  consists  in  receiv- 
ing the  image  thrown  by  a  camera  obscura  upon  a  glass 
plate  covered  with  a  layer  of  a  sensitive  preparation  of 
silver,  and  as  the  silver  salt  is  only  decomposed  when  it 
is  exposed  to  the  light,  and  in  proportion  also  to  the 
brilliancy  of  the  light,  a  permanent  image  is  fixed  upon 
the  plate. 


PHOSPHORESCENCE.  195 

Bail}'  experience  shows  that  the  moie  refrangible 
rays  are  more  active  in  producing  photographic  effects 
than  the  less  refrangible ;  a  blue  coat,  for  example, 
comes  out  very  bright  in  a  photograph,  a  red,  on  the 
other  hand,  very  dark  ;  although,  looked  at  directly,  the 
former  appears  to  the  eye  the  darker  of  the  two.  The 
most  immediate  key  to  the  action  of  the  different  kinds 
of  rays  is  obtained  when  we  photograph  the  solar 
spectrum  itself.  The  red,  yellow,  and  the  greater  part 
of  the  green  rays  are  then  seen  to  be  completely  without 
action,  whilst  the  blue,  violet,  and  especially  the  ultra- 
violet part  of  the  spectrum  are  depicted  sharply  with 
all  their  dark  lines.  Photography  acts  upon  the  ultra- 
violet rays  still  more  than  fluorescence ;  it  constitutes  a 
means  not  only  of  making  this  part  of  the  spectrum 
visible,  but  also  of  fixing  it  permanently. 

These  groups  of  more  refrangible  rays,  namely,  the 
blue,  violet,  and  ultra-violet,  may  fairly  be  characterised 
by  the  term  '  photographic  rays.'  When,  as  is  frequently 
done,  they  are  called  '  chemical  rays,'  the  exclusive 
power  is  incorrectly  ascribed  to  them  of  acting  chemi- 
cally. Their  chemical  action  does  not  depend,  as  might 
be  inferred  from  the  term  '  chemical  rays,'  upon  any 
special  chemical,  or  as  it  has  also  been  called  ( actinic  ' 
property  inherent  in  them  in  opposition  to  the  other 
rays,  but  simply  upon  the  circumstance  that  all  easily 
decomposed  salts  possess  the  property  of  absorbing  the 
more  refrangible  rays  whilst  they  allow  the  less  re- 
frangible to  pass  through  them. 

That  the  less  refrangible  rays  are  really  capable  of 
exerting  a  chemical  action  was  demonstrated  by  H. 
Vogel.  By  the  addition  of  certain  anilin  colouring 
matters  to  bromide  of  silver  he  was  able  to  produce 


196  OPTICS. 

photographic  plates  which  were  sensible  for  the  green, 
yellow,  and  red  colours.  For  as  these  colouring  matters 
absorb  the  above-mentioned  rays  they  undergo  a  chemi- 
cal change  which  enables  them  to  decompose  the 
bromide  of  silver. 

The  most  conspicuous  example  of  the  chemical  action 
of  the  less  refrangible  rays  is,  however,  afforded  by 
nature  herself.  Plants  draw  the  whole  of  the  carbon 
they  require  for  their  growth  from  the  air,  and  this  they 
effect  by  the  decomposition  of  carbonic  acid  gas,  which 
they  break  up  into  carbon,  which  remains  as  part  of 
the  plant,  and  oxygen  which  is  returned  to  the  atmo- 
sphere in  the  gaseous  form.  This  action,  so  important 
for  the  welfare  of  plants,  is  completed  only  in  the 
green  (chlorophyll-holding)  parts  of  the  plants  under 
the  influence  of  the  solar  light.  By  means  of  researches 
on  different  coloured  light  it  is  now  ascertained  that 
those  rays  which  cause  the  liveliest  elimination  of 
oxygen  belong  to  the  less  refrangible  half  of  the 
spectrum. 


ACTION   OF    HEAT. 


CHAPTEE   XIV. 

ACTION  OF  HEAT. 

83.  THE  surface  of  the  earth  is  not  only  illumi- 
nated by  the  solar  rays,  but  it  is  also  warmed  by  them. 
It  is  clear  from  what  has  been  said  that  rays  which  are 
reflected  from  the  surface  of  any  body,  or  which  are 
transmitted,  cannot  have  any  action  in  warming  it. 
It  is  by  the  retained  or  absorbed  rays  alone  that  it  can 
be  warmed. 

From  this  point  of  view  it  is  not  difficult  to  appre- 
hend the  different  behaviour  of  bodies  in  regard  to  their 
capacity  of  being  warmed  by  the  solar  rays. 

Air  being  transparent  allows  the  solar  rays  to 
traverse  it  without  diminution  of  their  intensity ;  it  is 
consequently  warmed  by  them  only  to  a  very  insignifi- 
cant degree.  Hence  the  upper  regions  of  the  air, 
although  they  receive  the  solar  rays  at  first  hand,  are 
so  cold  that  even  in  the  tropics  the  summits  of  high 
mountains  are  covered  with  everlasting  snow.  The 
warming  of  the  air  is  mainly  due  to  the  heat  it  receives 
from  the  heated  surface  of  the  earth  below,  which 
gradually  communicates  the  heat  it  has  obtained  by 
absorption  to  the  strata  of  air  in  immediate  contact 
with  it. 

Bodies  with  polished  surfaces,  which  reflect  the 
greater  part  of  the  rays  falling  upon  them,  and  trans- 


OF1ICS. 

parent  colourless  bodies,  which  almost  wholly  transmit 
such  rays,  undergo  only  slight  heating.  On  the  con- 
trary, rough  surfaces,  that  is  to  say,  surfaces  incapable 
of  much  reflexion,  arid  dark  colours,  or  those  which 
possess  high  power  of  absorption,  are  conditions  that 
favour  the  heating  action  of  light. 

Any  substance  therefore  will  become  heated  by  radia- 
tion to  the  greatest  degree  when  its  surface  is  made 
rough  and  completely  black,  so  that  it  can  absorb  all 
the  rays  falling  upon  it.  This  object  is  best  attained  by 
coating  the  substance  with  lampblack. 

Thus,  for  example,  if  two  thermometers  be  exposed 
to  the  sun,  the  bulb  of  one  of  which  is  blackened 
whilst  the  other  is  bright,  the  former  will  show  a  higher 
temperature  than  the  latter. 

Herschel  first  suggested  that  with  the  aid  of  such  a 
blackened  thermometer  the  calorific  power  of  the  different 
coloured  rays  of  the  spectrum  could  be  tested.  When 
he  exposed  a  thermometer  successively  to  the  several 
rays  he  found  that  the  red  were  much  hotter  than  the 
blue,  and  that  even  in  the  dark  region  on  the  near  side  of 
the  red  end  a  considerable  elevation  of  temperature  was 
still  observable. 

An  ordinary  thermometer,  however,  is  not  sensitive 
enough  to  follow  and  determine  all  the  degrees  of  varia- 
tion of  temperature  in  the  spectrum.  But  we  possess 
in  the  Thermopile  an  instrument  admirably  adapted  for 
such  delicate  researches. 

If  rods  of  antimony  and  bismuth  be  soldered  to- 
gether in  the  manner  shown  in  fig.  127,  so  that  the  first, 
third,  and  fifth,  &c.,  or  generally  the  odd  numbered 
joints,  are  turned  in  one  direction,  whilst  the  even  TIU  in- 
bered  joints  are  turned  to  the  opposite  side,  and  if  the 


ACTION   OF  HEAT. 


199 


FIG.  127. 


it 

Construction  of 
the  thermo- 
pile. 


FIG.  128. 


terminal  rods  a  and  b  are  connected  by  a  wire,  an  electric 
current  is  excited  in  this  as  soon  as  one  series  of  joints, 
as,  for  example,  the  odd  numbered  joints, 
are  heated. 

These  groups  of  rods  are  enclosed  in 
a  brass  case  (fig.  128),  so  that  the  odd 
numbered  joints  lie  between  the  slit  a  b, 
whilst  the  terminal  rods  are  connected  with 
the  binding  screws  c  and  d.  The  joints  are 
blackened,  to  favour  as  far  as  possible  the  absorption 
of  the  rays  falling  upon  them.  This  apparatus  is 
termed  a  Thermopile  ;  and  because  the  joints  are 
arranged  in  a  straight  line,  a  b,  a 
linear  Thermopile. 

The  strength  of  the  thermo-electric 
current  traversing  the  wire  connecting 
the  poles  is  proportional  to  the  heat 
applied  to  the  joints.  From  the  in- 
tensity of  the  current  may  be  esti- 
mated the  degree  of  heat  to  which  the 
joints  have  been  exposed. 

For  the  measurement  of  the  in- 
tensity of  the  current  the  instrument 
termed  the  Galvanometer,  and  depicted  Linear  therm<>piie. 
in  fig.  129,  is  employed.  A  copper  wire  covered  with 
silk  is  wound  round  and  round  a  frame  of  wood,  in  the 
interior  of  which  a  magnetic  needle  is  freely  suspended 
by  means  of  a  fibre  of  silk  from  the  cocoon.  The  ends  of 
the  wire  are  fixed  by  binding-screws.  A  second  magnetic 
needle,  firmly  connected  with  the  first,  is  placed  above 
the  frame,  and  plays  freely  over  a  circle  divided  into 
degrees.  The  two  needles  are  parallel  to  each  other, 
but  their  poles  point  in  opposite  directions.  By  this 


200 


OPTICS. 


means  they  are  retained  in  the  position  of  equilibrium  re- 
sulting from  the  magnetism  of  the  earth  with  very  slight 
FIG.  129.  force  only,  whilst  the  ac- 

tion of  the  current,  which 
exerts  its  influence  alike 
upon  both,  is  doubled.  The 
action  of  a  galvanic  cur- 
rent traversing  the  coil 
consists  in  causing  the 
needles  to  deviate  from 
their  position  of  equili- 
brium parallel  to  the  turns 
of  the  wire,  and  this  to 
an  extent  corresponding 
to  the  intensity  of  the  cur- 
rent. 

84  If  now  the  binding- 
screws  of  the  Thermopile 
are  connected  by  means  of 
wires  with  the  ends  of  the 
coil  of  the  Galvanometer,  and  the  Thermopile  be  placed 
in  the  violet  end  of  a  solar  spectrum  thrown  by  a  flint- 
glass  prism,  it  will  be  found  that  the  deviation  of  the 
galvanometric  needle  is  extremely  small ;  but  it  will  be 
observed  that  the  deviation  progressively  increases  a« 
the  Thermopile  is  gradually  moved  towards  the  red 
end  of  tne  spectrum,  and  that  it  even  becomes  still 
greater  in  the  dark  region  on  this  side  of  the  red  till  a 
point  is  reached  which  is  as  distant  from  the  line  B  as 
this  is  from  the  line  D.  From  this  point  onwards 
it  gradually  again  diminishes,  though  it  may  be  fol- 
lowed for  a  considerable  distance  into  the  dark  region. 
Thus  it  is  seen  that  amongst  the  rays  emitted  by 


Galvanometer. 


ACTION  OF  HEAT. 


201 


the  sun  there  are  some  of  still  less  refrangibility  than 
the  extreme  red  rays,  and  these  may  be  termed  the 
ultra-red  rays.  They  are  recognised  by  their  calorific 
action  alone  j  they  are  imperceptible  to  the  eye,  for 
the  reason  that  they  are  absorbed  by  the  fluids  of  the 
eye,  and  never  reach  the  retina.*  On  this  account  they 
are  sometimes  termed  the  '  dark  calorific  rays.' 

In  order  to  obtain  a  general  view  of  the  calorific 
action  of  the  different  parts  of  the  spectrum,  perpen- 
dicular lines  must  be  FIG.  iso. 
erected  upon  the  long 
axis  of  a  spectrum 
(fig.  130)  of  a  height 
corresponding  to  the 
measured  heating 
power  of  that  part 
of  the  spectrum.  By 
joining  the  apices  of 
these  perpendiculars  we  obtain  a  curved  line  which 
exhibits  the  varying  amount  of  the  calorific  power  in 
different  parts. 

In  the  spectrum  of  a  flint-glass  prism  the  apex  of 
the  thermotic  curve — that  is  to  say,  the  place  of  greatest 
heat-effect — is  situated,  as  is  shown  above,  outside  the 
apparent  spectrum  in  the  ultra-red  region. 

If  the  spectrum  thrown  by  a  prism  and  a  lens  of 
rock  salt  be  now  examined,  the  thermotic  action  will 
be  found  exactly  equal  in  the  visible  part  of  the  spectrum 
to  that  of  the  corresponding  part  of  a  flint  prism  spec- 
trum ;  in  the  ultra-red  region,  however,  the  thermotic 
curve  of  the  rock-salt  spectrum  rises  above  that  of  the 


Heat-curves  of  the  spectra  thrown  by 
flint  glass  and  rock  salt. 


*  According  to  the  researches  of  Briicke  and  Knoblauch. 


202  OPTICS. 

flint  spectrum,  and  its  highest  point  is  still  less  re- 
fracted (fig.  130,  upper  curve).  It  appears  therefore 
that  flint  glass  is  less  diathermanous  for  the  dark  heat- 
rays  than  rock  salt.  By  experiments — an  account 
of  which  would  lead  us  too  far  astray — it  may  be  shown 
that  rock  salt  allows  the  dark  rays  to  pass  without  let 
or  hindrance,  whilst  most  other  bodies,  even  if  they 
happen  to  be  quite  transparent  for  luminous  rays, 
absorb  them  to  a  greater  or  less  extent.  If  it  be 
required  therefore  to  compare  the  spectra  from  various 
sources  of  light  in  regard  to  their  thermotic  action,  the 
prisms  and  lenses  should  be  made  of  rock  salt. 

We  thus  find,  for  example,  that  the  electric  light 
from  carbon  points  is  relatively  much  richer  in  dark 
thermotic  rays  than  sunlight.  At  a  point  of  its  ultra- 
red  spectrum  which  is  at  the  same  distance  from  it  as 
the  commencement  of  the  green  upon  the  visible  side, 
the  thermotic  action  is,  according  to  Tyndall,  five  times 
as  great  as  that  of  the  red  rays. 

The  stronger  thermotic  action  of  the  ultra-red  rays, 
in  comparison  with  that  of  the  luminous,  is  strikingly 
Flo  131  shown    by   the    following   experi- 

ment : — Two  spherical  flasks  are 
taken,  one  of  which  contains  a 
transparent  solution  of  alum,  which 
permits  all  visible  or  luminous  rays 
to  pass  through  it  without  inter- 
ruption, whilst  it  absorbs  the  in- 
Action  of  the  invisible  visible  thermotic  rays.  The  other 

thermotic  n.ys.  .        £11     ,         ..,  ...  _    .     ,. 

is   filled  with  a  solution  of  iodine 

in  carbon  bisulphide,  which  appears  black  because  it  is 
completely  opaque  for  luminous  rays ;  it  transmits,  on 
the  contrary,  the  thermotic  rays.  If  the  alum  flask  be 


ACTION   OF  HEAT.  203 

placed  before  the  aperture  of  the  electric  lamp,  it 
collects,  acting  like  a  lens,  the  luminous  rays  into 
a  caustic  of  dazzling  brilliancy)  the  heating  power  of 
which  however  is  but  small,  for  a  pellet  of  gun-cotton 
placed  in  the  focus  will  not  explode.  The  flask  con- 
taining the  black  fluid  (fig.  131),  on  the  contrary, 
unites  exactly  in  the  same  way  the  dark  rays  into  an 
invisible  focal  point,  Ihe  heat  of  which  not  only  causes 
the  gun-cotton  instantaneously  to  explode,  but  even 
raises  a  piece  of  platinum  foil  to  red  heat. 

85.  Every  source  of  light  gives  off,  besides  its 
luminous  rays,  dark  rays  of  small  refrangibility.  Hot 
bodies,  on  the  other  hand,  not  heated  sufficiently  to 
glow,  emit  only  dark  rays.  In  the  Thermopile  wTe 
possess  a  means  of  demonstrating  the  presence  of  such 
rays  and  investigating  their  behaviour.  And  the  results 
of  numerous  researches  have  shown  that  the  dark  rays 
obey  the  same  laws  as  the  bright  ones  ;  they  undergo 
reflexion  from  polished  surfaces  as  from  a  mirror,  whilst 
they  are  diffusely  reflected  from  rough  surfaces.  They 
course  in  a  straight  direction  through  one  and  the  same 
medium,  but  are  refracted  when  they  enter  another 
medium,  their  refrangibility  agreeing  with  that  of  the 
ultra-red  portion  of  the  spectrum. 

A  solid  body,  as  for  example  a  platinum  wire,  which 
is  gradually  raised  to  an  intense  heat,  first  emits  dark 
ultra-red  rays ;  as  soon  as  it  begins  to  glow,  it  emits  in 
addition  the  extreme  red  rays.  At  a  bright  red  heat  its 
spectrum  extends  as  far  as  F,  and  at  a  white  heat  it 
gives  off  all  kinds  of  rays  as  far  as  H. 

All  these  facts  demonstrate  that  no  other  difference 
exists  between  the  dark  heat-rays  and  the  luminous 
rnys  than  the  gradual  and  progressive  increase  of 


204  OPTICS. 

refrangibility ;  the  former  do  not  differ  from  the  latter 
otherwise  than  the  red  rays  differ  from  the  yellow,  or 
the  yellow  from  the  green.  The  invisibility  of  the 
former  does  not  consist  in  any  peculiarity  of  the  rays 
themselves,  but  is  dependent  on  the  nature  of  our  eyes, 
the  fluids  of  which  are  opaque  for  the  ultra-red  rays. 

The  dark  rays  are  percepllble  to  us  only  through 
the  sensation  of  warmth  they  give  to  us  ;  the  luminous 
rays,  on  the  contrary,  act  simultaneously  on  two  organs 
of  sense — upon  the  nerves  of  common  sensibility  or 
touch  as  heat,  and  upon  the  eye  as  light.  Every  ray  of 
light  is  thus  at  the  same  time  a  ray  of  heat.  We  are 
incapable,  for  example,  of  separating  the  heating  effect 
caused  by  the  yellow  light  of  Sodium  from  its  illu- 
minating power.  It  gives  no  rays  of  such  low  refrangi- 
bility  that  they  produce  only  the  effects  of  heat,  and 
not  of  light. 

Light  and  radiant  heat  are  therefore,  as  effects  of 
one  and  the  same  cause,  to  be  distinguished  from  each 
other  not  by  any  peculiarity  of  their  own,  but  only  by 
us  as  different  forms  of  sensation.  The  same  individual 
ray  calls  up  in  us,  according  to  the  nerve-path  through 
which  the  impression  it  makes  is  conducted  to  the  seat 
of  our  consciousness,  sometimes  a  sensation  of  light  and 
sometimes  of  heat,  just  as  a  drop  of  vinegar  applied  to 
the  tongue  tastes  sour,  but  if  brought  into  contact 
with  a  sore  place  on  the  skin,  produces  a  sensation  of 
burning ;  or  as  a  tuning  fork  when  struck  produce  s  a 
sensation  of  sound  in  the  ears,  but  a  feeling  of  vibration 
to  the  hand  in  contact  with  it. 

'86.  If  now  a  general  view  of  the  solar  spectrum 
throughout  its  whole  extent  be  taken,  it  is  seen  to  be 
composed  of  three  portions  of  nearly  equal  length — 


ACTION   OF   HEAT.  205 

the  ultra-red,  the  luminous,  and  the  ultra-violet 
portion. 

In  the  figure  below  (fig.  132)  three  curved  lines  are 
drawn  above  the  spectrum,  of  which  that  marked  by 
///  is  the  curve  that  we  now  know  of  heat ;  the  curve  • 

//  in  like  manner  expresses  the  chemical  action  on  a 
mixture  of  chlorine  and  hydrogen  and  the  salts  of 
silver ;  and  the  curve  I  gives  the  brilliancy  of  the  illu- 

JrxJU' 
FIG.  132. 


K        OF        n    B 

Light,  heat,  and  photographic  action  of  the  solar  spectrum. 

mination  within  the  limits  of  the  visible  spectrum. 
Prom  this  drawing  it  is  evident  that  the  maximum 
amount  of  light  is  in  the  yellow,  the  maximum  of  the 
photographic  action  is  in  the  violet,  and  finally,  the 
maximum  heat  is  in  the  ultra-red. 

In  reference  to  the  rays  themselves,  these  three 
curves  have  a  very  different  signification.  It  is  clear 
that  the  action  which  a  ray  exerts  upon  a  body  is 
determined  on  the  one  hais^  by  the  intensity  or  energy 
of  the  ray,  and  on  the  vther  by  the  capacity  for 
absorption  of  the  body.  However  great  the  intensity  of 
a  ray  may  be,  it  will  exert  no  influence  upon  a  body 
which  will  not  absorb  it.  Thus,  for  example,  the  red 
rays,  however  intense  they  may  be,  exert  no  influence 
on  a  mixture  of  hydrogen  and  chlorine,  or  sensitive 
silver  salts,  because  these  substances  do  not  absorb 
them. 

Each  of  the  curves  I  and  II  therefore  expresses  the 


206  OPTICS. 

co-operation  of  two  actions — the  intensity  of  the  rays 
and  the  capabiliiy  of  absorption  of  the  retina,  or  of  a 
photographic  plate — which  is  very  different  for  different 
kinds  of  rays.  They  afford  us  therefore  but  little 
direct  information  on  either  point.  The  curve  177 
shows  the  heating  influence  which  each  part  of  the 
spectrum  exerts  upon  the  blackened  surface  of  the 
Thermopile.  Now  lampblack  behaves  as  an  almost 
perfectly  black  body  to  all  kinds  of  rays  alike,  since 
it  completely  absorbs  them  all,  and  becomes  heated  in 
proportion  to  their  intensity.  The  thermotic  curve 
shows  therefore  the  intensity  of  the  radiation  which 
falls  on  each  part  of  the  spectrum  free  from  the  in- 
fluence of  any  special  capacity  for  absorption.  It  is 
therefore  to  be  regarded  as  the  true  curve  of  intensity  of 
the  prismatic 


FRESNEL'S  MIRROR  EXPERIMENT. 


207 


FIG.  133. 


CHAPTEE  XV. 

MIRROR    EXPERIMENT    OF    FRESNEL. 
UiNDULATORY    MOVEMENT. 

87.  THE  reader  has  hitherto  had  his  attention  con- 
fined to  the  experimental  investigation  of  the  laws 
of  the  phenomena  of  light  without  speculating  as 
to  what  light  essentially  is.  A  series  of  phenomena 
now  present  themselves 
which  raise  again  this 
question  of  the  nature 
of  light,  and  at  the 
same  time  afford  the 
means  of  answering  it. 
Let  two  mirrors,  A  B  and 
BC  (fig.  133),  be  made 
of  black  glass  and  be  so 
placed  as  to  meet  at  the 
vertical  slit,  B,  the  one, 
B  C,  being  permanently 
fixed  in  a  wooden  frame 

(Holzklotzchen)  which  can  be  moved  along  a  ver- 
tical rod  and  fastened  by  a  wooden  screw  T,  whilst  the 
other,  A  B,  is  revolvable  by  means  of  the  screw  8  around 
the  angle  J5by  means  of  the  hinge  attached  to  it.  The 
moveable  mirror  is  to  be  placed  in  such  a  position  that 
15 


Fresnel's  mirror. 


208 


OPTICS. 


its  plane  forms  a  very  obtuse  angle  (not  differing1  much 
from  180°)  with  that  of  the  fixed  mirror. 

A  sharply  defined  point  of  light  is  required,  and  may 
be  obtained  by  letting  the  solar  rays  proceeding  from  a 
Heliostat  fall  upon  a  lens  (fig.  134)  of  short  focal 
distance,  which  unites  them  into  a,  focus  P.  The 
luminous  point  P  emits  rays  which  strike  both  mirrors  ; 
from  the  mirror  A  B  they  are  so  reflected  that  they 


FIG. 134. 


Fresnel's  mirror  experiment. 

appear  as  if  they  came  from  the  image-point  M  of  this 
mirror.  The  mirror  B  C,  on  the  other  hand,  reflects  the 
rays  as  if  they  proceeded  from  its  image-point  N".  In 
order  that  the  two  mirrors  may  each  have  only  one 
reflecting  surface  and  have  only  one  image-point,  they 
must  be  made  of  black  glass  or  of  metal. 

From  these  mirrors  two  cones  of  light  Mm  mf  and 
Nnn  are  obtained,  which  appear  to  proceed  from  the 
points  M  and  N.  They  have  the  space  Bmn  (shaded 
in  the  figure)  common  to  both,  so  that  the  field  between 


FRESNEL'S  MIRROR  EXPERIMENT.      WAVE-MOTION.      209 

*n  and  n  upon  the  screen  m'  n'  situated  in  the  path  of 
the  reflected  ray  receives  light  simultaneously  from 
the  two  cones  of  light.  In  this  middle  area  a  series  of 
vertical  dark  lines  are  perceived,  but  if  one  of  the  glasses 
be  covered  the  lines  immediately  vanish  and  the  area 
which  now  receives  only  the  light  from  the  opposite 
mirror  appears  to  be  uniformly  illuminated  throughout 
its  whole  extent.  The  lines  however  immediately 
reappear  if  the  cover  be  removed,  and  to  the  light 
proceeding  to  the  screen  from  the  point  M  is  added 
that  also  which  proceeds  from  the  point  N. 

It  has  thus  been  demonstrated  that  light  added  to  1 1 
light  may,  under  certain  circumstances,  cause  darkness. 

If  by  turning  the  screw  S  (fig.  133)  the  angle  of 
the  two  mirrors  be  made  less  obtuse,  the  lines  become 
narrower  and  closer  together  till  they  ultimately  become 
so  fine  that  they  can  no  longer  be  distinguished. 
Hence  to  render  the  lines  distinctly  perceptible  the 
angle  between  the  two  mirrors  must  be  very  obtuse,  or 
what  comes  to  the  same  thing,  the  mirror  images  M 
and  N  must  be  very  closely  approximated. 

Instead  of  making  the  experiment  with  a  screen  so 
that  many  can  see  it  at  the  same  time,  any  individual 
may  observe  it  directly  by  making  his  retina  take  the 
place  of  the  screen.  This  subjective  method  of  observa- 
tion has  the  advantage  that  a  feeble  source  of  light  may 
be  employed  ;  and  then,  if  the  homogeneous  light  of 
the  Sodium  flame  be  used,  the  entire  field  of  vision  may 
be  observed  to  be  filled  with  numerous  vertical  and 
completely  black  lines. 

88.  The  just-described  mirror  experiment  of  Fres- 
uel,  named  after  the  genial  physicist  who  conceived 
it,  teaches  that  light  combined  with  light  may,  under 


210  OPTICS. 

certain  circum stances,  produce  darkness.  What  then 
must  be  understood  by  the  term  '  light,'  to  enable  this 
apparent  paradox  to  be  explained  ? 

This  much  is  certain,  that  every  luminous  body 
must  be  regarded  as  the  seat  of  a  motion  which  is  by 
some  means  propagated  to  our  optic  nerves  and  arouses 
in  them  the  sensation  of  brightness. 

Two  modes,  however,  are  only  known  in  which  move- 
ment may  be  propagated  from  one  point  of  space  to 
another. 

The  first  mode  is  the  immediate  transference  of  motion 
in  which  the  moved  body  itself  or  parts  of  the  same 
traverse  the  space  between  the  two  points,  as  when  a 
cannon  ball  flies  to  its  goal  from  the  cannon. 

The  second  mode  of  transference  takes  place  medi- 
ately through  an  elastic  medium  intervening  between 
the  two  points,  in  which  medium  the  body  originally 
in  motion  excites  a  vibratory  movement  that  is  propa- 
gated from  particle  to  particle,  it  may  be  to  a  great 
distance,  without  a  particle  of  the  originally  moving 
body  itself  or  any  portion  of  the  propagating  medium 
moving  from  its  original  position  to  any  considerable 
extent.  This  process  is  called  undulatory  movement. 

As  an  example  of  the  former,  the  sense  of  smell 
may  be  taken,  which  is  excited  by  the  immediate 
transference  of  particles  of  the  odorous  material  to  the 
olfactory  organ.  If  a  flask  containing  some  ainmo- 
niacal  gas,  which  is  colourless,  be  opened,  those  near 
it  quickly  perceive  the  stimulating  odour  of  the  gas, 
whilst  it  is  only  perceived  by  those  who  are  more 
distant  after  the  lapse  of  some  time.  It  would  be  easy 
to  demonstrate  by  appropriate  tests  the  presence  of 
particles  of  ammonia  even  in  the  furthest  corner  of  a 


FRESNEL'S   MIRROR   EXPERIMENT.      WAVE-MOTION.      211 

room.  The  smell  is  perceived  still  more  strongly  if  a 
second  flask  be  opened,  so  that  the  number  of  particles 
of  ammonia  present  in  the  air  is  increased ;  it  would, 
however,  be  needless  to  do  this,  since  all  must  be  satisfied 
that  the  sense  of  smell  is  excited  by  particles  of  th«? 
odorous  material  which  come  into  direct  contact  with 
the  olfactory  organ,  and  that  by  increase  of  the  effective 
particles  alone  can  the  intensity  of  the  sensation  be 
augmented. 

Another  of  our  senses,  hearing,  on  the  other  hand, 
receives  its  impressions  through  the  second  mode  of 
propagation,  since  every  resounding  body  puts  the  air 
around  it  into  undulatory  movement.  If  a  bell  be  struck 
its  sound  is  heard  simultaneously  with  the  blow.  The 
blow  makes  the  bell  vibrate,  that  is  to  say,  causes  its 
particles  to  make  rapid  to  and  fro  movements  or  vibra- 
tions which  are  felt  by  the  hand  in  contact  with  it  as 
a  trembling.  The  vibration  communicates  itself  in  the 
first  instance  to  the  particles  of  air  in  immediate 
contact  with  the  bell,  and  as  these  move  to  and  fro  in 
the  same  rapid  manner  they  produce  the  same  effect 
upon  the  particles  of  the  next  adjacent  layer  of  air  as 
the  bell  itself,  and  set  them  in  motion.  In  this  way  the 
vibratory  movement  is  propagated  with  great  rapidity 
from  one  layer  of  air  to  another,  and  finally,  on  reach- 
ing the  ear,  excites  in  the  auditory  nerve  the  sensation 
of  sound.  But  it  is  certain  that  neither  particles  of  the 
bell  itself,  nor  even  particles  of  the  air  immediately 
surrounding  the  bell,  penetrate  the  ear ;  if  they  did,  as 
sound  travels  at  the  rate  of  1,116  feet  in  the  second, 
they  would  strike  on  the  tympanum  with  a  velocity 
exceeding  that  of  the  most  violent  hurricane.  An 
extremely  simple  experiment  may  now  be  considered, 


212  oracs. 

which  may  be  shown  with  two  perfectly  similar  organ - 
pipes  standing  on  a  wind-chest  common  to  both.  If 
each  pipe  be  made  to  speak  separately  both  will  give 
precisely  the  same  fundamental  note.  Tf,  now,^  both 
pipes  be  sounded  together,  exactly  the  opposite  occurs 
to  what  might  be  expected ;  instead  of  the  fundamental 
note  being  increased  in  intensity  it  is  remarkably 
weakened,  so  much  so,  indeed,  that  at  a  little  distance 
from  the  pipes  the  fundamental  note  is  no  longer 
audible. 

From  this  circumstance1  the  same  conclusion  is 
drawn  in  regard  to  sound,  which  unquestionably  con- 
sists in  an  undulatory  movement,  as  was  done  in  the 
case  of  the  light  in  the  mirror  experiment  of  Fresnel, 
namely,  that  sound  added  to  sound  may,  under  certain 
circumstances,  produce  silence. 

89.  Through  which  of  the  two  possible  modes  of 
propagation  does  the  movement  that  we  call  '  light ' 
spread  ?  Are  our  eyes  when  we  look  at  the  sun  struck 
by  particles  of  a  luminous  material  uninterruptedly 
emitted  by  that  luminous  body  ?  Or  do  the  rays  of 
light  consist  of  a  vibratory  movement  which  strikes 
upon  our  retina  in  the  form  of  minute  waves — in  other 
words,  is  the  process  of  seeing  analogous  to  that  of 
smelling  or  of  hearing? 

The  choice  between  these  two  modes  of  explaining 
the  phenomena,  after  what  has  been  said,  cannot  be 
difficult.  On  the  supposition  of  there  being  a  luminous 
substance  (emission  theory),  the  fact  that  light  super- 
added  to  light  can  produce  darkness  is  wholly  in- 
explicable. On  the  other  hand,  a  case  has  been  cited 
in  which  an  undulatory  movement  co-operating  with  a 
similar  undulation  produces  such  &n  effect,  and  we  shall 


FRESNEL'S  MIRROR  EXPERIMENT.      WAVE-MOTION.      213 

see  immediately  that  this  follows  necessarily  from  the 
very  nature  of  undulatory  movement.  It  will,  more- 
over, be  seen  that  the  admission  of  luminous  waves 
(undulatory  theory)  gives  a  perfectly  satisfactory 
explanation,  not  only  of  the  phenomena  in  question, 
but  of  the  great  majority  of  the  phenomena  of  light, 
and  is  opposed  to  none  of  them,  whilst  the  conception 
of  a  luminous  aether  or  substance  has  long  been  negatived 
by  facts. 

As  the  view  that  light  is  itself  a  material  substance 
is  set  aside,  and  it  is  regarded  as  an  undulatory 
movement,  it  becomes  necessary  to  admit  the  existence 
of  a  material  in  which  the  waves  of  light  can  propagate 
themselves.  The  air,  in  which  the  waves  of  sound 
spread,  cannot  be  coincideiitly  the  carrier  of  luminous 
waves,  for  it  only  forms  a  thin  investment  around  our 
earth,  and  perhaps  other  heavenly  bodies  ;  whilst  in 
the  immeasurable  depths  of  space  through  which  the 
light  of  the  sun  and  the  fixed  stars  .reaches  ns  no  air  is 
present.  It  must  therefore  be  admitted  that  the 
universe  is  filled  with  an  elastic  material  which  is  so 
rarefied  that  it  opposes  no  appreciable  resistance  to  the 
movement  of  the  celestial  bodies.  This  attenuated 
elastic  matter  is  called  6  ^Ether.' 

90.  The  waves  of  water  afford  an  excellent  repre- 
sentation of  the  phenomena  of  wave-movement.  If  a 
stone  be  thrown  into  water  at  rest  a  circular  depression 
forms  around  the  point  struck  which  spreads  wider  and 
wider  with  uniform  velocity.  In  the  meanwhile  an 
elevation  has  formed  at  the  point  where  the  stone 
entering  the  water  had  originally  caused  a  depression ; 
then  as  this  sinks  back  to  its  original  level  it  produces 
a  wall-like  circular  elevation  around  it,  which  follows 


214  .  OPTICS. 

up  the  preceding  circular  depression  with  equal  velocity. 
Whilst  the  fluid  continues  its  up-and-down  movement 
at  the  point  struck,  fresh  alternately  depressed  and 
elevated  wave  rings  appear  to  proceed  from  this  middle 
point,  or,  as  it  is  customary  to  call  them,  wave  eleva- 
tions (crests)  and  depressions  (sinuses)  (Wellenthaler 
and  Wellenberge),  are  formed,  which,  owing  to  their 
constantly  spreading  more  and  more  widely  give  the 
illusory  appearance  of  the  fluid  streaming  ojut  on  all 
sides  from  the  middle  point. 

That  no  such  streaming  movement  does  really  occur 
may  easily  be  demonstrated  by  observing  any  small 
object  accidentally  floating  on  the  water,  as  for  example, 
a  piece  of  wood.  This,  as  the  crests  and  sinuses  of 
the  waves  spread  beneath  it,  merely  rises  and  falls 
without  materially  changing  its  original  position, 
making  the  oscillation  of  the  particles  of  water  imme- 
diately beneath  it  apparent. 

The  cause  of  the  waves  of  water  is  the  force  of 
gravity  which  is  exerted  after  each  disturbance  of  the 
equilibrium  to  restore  the  fluid  to  its  original  horizontal 
plane.  Whilst  the  particles  of  the  water  first  struck 
and  depressed  by  the  stone  are  soon  again  compelled  to 
rise,  they  oblige  at  the  same  time  the  easily  moveable 
adjoining  particles  to  descend  in  order  that  the  depres- 
sion which  was  formed  may  be  again  filled  up.  As 
every  particle  begins  to  fall  somewhat  later  than  the 
immediately  antecedent  one,  a  circular  wave-depression 
spreads  round  the  central  point  of  excitation,  which 
attains  its  full  development  at  the  moment  in  which 
the  particle  struck  in  its  ascending  movement  has 
again  attained  its  original  level.  It  does  not  however 
here  come  to  rest,  but  continues  its  movement  upwards 


FRESNEL'S  MIRROE  EXPERIMENT.      WAVE-MOTION.      215 

above  the  horizontal  plane  of  the  water  until  the  force 
of  gravity  acting  in  opposition  has  exhausted  its  up- 
ward directed  velocity,  and  it  swings  back  again  to  the 
level.  In  the  meanwhile  the  neighbouring  particks, 
which  exactly  imitate  the  undulating  movement  of  the 
first  disturbed  particles  in  the  same  period  of  time, 
form  a  wave- crest  which  is  fully  developed  at  the 
moment  in  which  the  first  particles  have  again  reached 
the  plane  in  their  descending  movement. 

And  now,  when  the  particle  first  excited  has  com- 
pleted one  entire  vibration,  and  is,  as  at  the  com- 
mencement of  its  movement,  again  about  to  leave  its 
position  of  equilibrium  in  order  to  descend,  it  has 
around  it  a  complete  wave,  consisting  of  a  wave  depres- 
sion and  a  wave  crest.  This  wave  as  it  spreads  produces 
the  second  to-and-fro  movement  of  each  particle,  and 
every  subsequent  complete  wave  acts  in  a  similar 
manner,  and  as  the  new  waves  immediately  follow 
those  antecedent  to  them,  a  circular  system  of  waves  is 
developed  around  the  central  point  of  excitation. 

91.  Every  straight  line  drawn  from  the  middle  point : 
of  a  system  of  waves  upon  the  surface  of  the  water 
regarded  as  horizontal  is  termed  a  wave  ray.  All  par- 
ticles of  water  which  when  at  rest  lie  on  this  straight 
line  are  now  elevated,  now  depressed,  according  to 
whether  they  for  the  moment  belong  to  a  wave  crest 
or  a  wave  depression,  and  form  therefore  in  their  serial 
succession  an  ascending  and  descending  sinuous  line. 
Such  a  wave-line,  granting  that  the  particles  rise  and 
fall  perpendicularly  to  the  ray  A  B,  is  represented  in 
tig.  135.  That  portion  of  a  ray  which  is  included  in  a 
i  complete  wave,  that  is  to  say,  which  includes  a  wave 
crest  and  a  wave  depression,  or  any  portion  of  it  equal 


216  OPTICS. 

to  this,  is  called  a  wave-length.  In  the  figure  we  have  for 
example  between  A  and  B  three  complete  wave-lengths, 
and  one  wave-length  between  b  and  c,  and  between  c 
and  d.  Those  particles  which  in  any  ray  are  separated 
from  one  another  one  or  several  complete  wave-lengths, 


FIG.  135. 


Undulatory  ray. 

are  at  any  moment  of  time  in  exactly  the  same  condition 
of  undulation,  their  movements  are  in  perfect  accordance 
with  each  other.  The  particles  b'  cf  and  d'9  for  example, 
which  are  distant  from  one  another  one  or  two  wave- 
lengths, have  all  three  arrived  at  their  greatest  height, 
and  are  about  to  descend.  Moreover,  the  particles  A 
and  By  the  distance  between  which  includes  three  wave- 
lengths, are  both  in  the  act  of  descending  through  their 
position  of  equilibrium. 

The  particles  b'  and/  on  the  other  hand,  which  are 
distant  from  each  other  a  half  wave-length,  are  in  just 
the  opposite  conditions  of  vibration.  For  whilst  the 
former  is  beginning  to  fall  from  its  highest  position, 
the  latter  is  just  about  to  rise  from  its  lowest  position. 
The  same  relation  occurs  between  the  particles  /"  and  d'. 
which  are  distant  from  each  other  three  half  wave- 
lengths. Speaking  generally,  it  is  clear  that  the  move- 
ments of  two  particles  the  distance  between  which  is 
an  unequal  multiple  of  a  half  wave-length  are  directly 
i  opposed. 


PHENOMENA  OF  INTERFERENCE.  253 


CHAPTER  XVI. 

PRINCIPLE  OF  INTERFERENCE.     CONSEQUENCES  OF 
FRESNEL'S*  EXPERIMENT. 

92.  WHAT  happens  if  two  wave-systems  meet  on 
the  same  fluid  surface? 

If  from  a  vessel  held  above  a  flat  pan  containing 
mercury  two  fine  streams  of  mercury  are  allowed  to  fall, 
each  produces  around  the  point  where  it  strikes  the 
surface  of  the  fluid  a  circular  system  of  waves.  As  the 
two  wave-systems  decussate  they  divide  the  surface  into 
a  regular  network  of  small  elevations  and  depressions, 
a  representation  of  which  is  attempted  in  fig.  136. 

If  the  light  of  the  sun  or  of  the  electric  lamp  be 
allowed  to  fall  upon  the  surface  of  the  mercury,  the 
reflexion  upon  a  screen  will  also  furnish  a  representation 
of  this  delicate  phenomenon. 

It  is  not  difficult  to  explain  the  effects  observed. 
At  all  points  where  two  wave  crests  meet,  the  surface 
of  the  fluid,  if  the  two  waves  are  equal,  rises  to  twice 
the  height,  and  where  two  depressions  meet  it  sinks 
to  double  the  depth.  At  those_  points  on  the  contrary 
where  a  wave  -erest  is  cut  by  a  sinus,  tlie  upheaving  and 
depressing  forces  are  in  equilibrium,  and  the  fluid  re- 
mains at  rest  at  its  original  level. 

In  a  fluid  set  in  motion  by  two  or  more  equal  or 
unequal  wave  systems,  every  particle,  speaking  gene- 


218 


OPTICS. 


rally,  undergoes  a  change  of  place,  which  is  the  sum  of 
all  the  movements  impressed  upon  it  by  the  several 
systems  of  waves  at  the  same  moment.  Of  course,  by  the 


FIG.  136. 


Interference  of  two  systems  of  waves. 

word  c  sum  '  the  so-called  algebraic  sum  is  meant,  that 
is  to  say,  the  elevations  are  regarded  as  positive,  the 
depressions  as  negative  values. 

In  other  words,  it  may  be  said  that  every  wave 
system  superimposes  itself  upon,  or  adds  itself  to,  a 
surface  already  moved  by  waves,  as  it  would  do  were  it 
acting  alone  on  the  surface  at  rest.  Every  wave  system 
forms  itself  unhindered  by  those  already  present,  and 


PHENOMENA   OF  INTERFERENCE.  219 

spreads  after  it  has  crossed  these  upon  the  still  quies- 
cent surface  of  the  water  as  if  it  had  suffered  no  inter- 
ruption. We  see,  for  example,  the  slight  wave  rings 
excited  by  the  falling  rain  drops  form  on  the  largei 
waves  raised  by  a  steamboat  just  as  well  as  upon  the  sea 
at  rest.  It  may  be  observed  again  that  these  waves, 
when  they  traverse  an  area  rippled  by  the  breeze,  take 
the  small  waves  on  their  back,  and  having  passed 
beyond  this  region  leave  these  last  behind  with  their 
original  form  unaltered. 

The  important  law  just  laid  down,  to  which  the 
processes  taking  place  in  the  co-operation  or  inter- 
ference of  two  or  several  systems  of  waves  are  subjected, 
is  termed  '  the  principle  of  interference.' 

93.  Returning  to  the  simplest  case  of  interference 
of  two  equal  systems  of  waves  represented  in  fig.  136,  it 
appears  that  an- explanation  can  be  given  of  the  move- 
ment occurring  at  each  point  of  the  surface  of  the  fluid, 
if,  instead  of  the  waves  themselves,  the  wave  rays  are 
kept  in  view.  If  we  consider,  for  example,  the  points 
5  ....  -V  lying  along  the  wall  of  the  vessel,  the  two 
rays  which  may  be  conceived  as  drawn  from  the  two 
middle  points  of  the  exciting  cause  of  them  to  the 
central  point  0  are  equal  to  each  other  in  length ;  the 
oscillating  movements  which  proceed  simultaneously 
from  each  of  these  centres  meet  therefore  in  the  point  Q 
under  equal  conditions  and  produce  the  greatest  pos- 
sible effect.  In  the  laterally  situated  point  1,  on  the 
other  hand,  two  rays  meet  which  are  about  half  a 
wave  different ;  the  forces  which  they  exert  upon  the 
point  are  therefore  equal  and  opposite  ;  the  point 
consequently  remains  at  rest.  The  same  occurs  at  3 
and  5,  where  the  difference  between  the  rays  cor- 


220  OPTICS. 

responds  respectively  to  3  half  and  5  half  wave-lengths. 
At  the  points  2  and  i,  on  the  contrary,  where  the  rays 
respectively  differ  one  or  two  entire  wave-lengths,  and 
thus  meet  under  equal  conditions  of  oscillation,  the 
liveliest  movement  takes  place.  The  intervening  points 
are  maintained  in  less  active  movement  by  pairs  of 
rays  of  all  possible  degrees  of  accordance  and  opposi- 
tion. 

The  points  1,  3,  5, 1',  3',  5' thus  remain  at 

rest  under  the  action  of  the  two  systems  of  waves. 
That  which  in  waves  of  fluid  is  rest,  is  in  waves  of 
sound  silence,  and  in  waves  of  light  darkness. 

it  is  scarcely  necessary  to  expressly  mention  here 
that  this  affords  a  complete  explanation  of  Fresnel's 
mirror  experiment,  and  that  fig.  136  is  a  sketch  of  it. 
[f,  for  example,  the  two  points  of  light  produced  by  the 
mirrors  M  and  N  (fig.  134)  be  regarded  as  centres  of 
origin  of  light  waves,  and  the  wall  5'  ....  5  as  the 
screen  for  receiving  them ;  and  if  it  be  further  con- 
sidered that  the  waves  of  light  expand,  not  only  circu- 
larly in  one  plane,  but  like  a  sphere  into  the  surround- 
ing sether,  it  will  be  understood  that,  in  consequence  of 
the  interference  of  the  two  systems  of  waves,  vertical 
dark  lines  must  appear  at  the  points  1,  3,  5  ....  1',  3', 
5',  and  bright  strise  at  the  points  2,  4  ....  2',  4'. 

But  why,  it  may  perhaps  be  now  asked,  should  the  two 
points  of  light  be  employed  in  a  roundabout  way  after 
their  reflexion  in  the  two  mirrors  ?  Would  it  not  be 
simpler  to  put  aside  the  mirrors,  and  use,  instead  of  the 
images  M  and  N  thrown  by  them,  two  luminous  points 
like  the  points  of  a  glowing  platinum  wire  ?  The 
answer  to  this  question  is  obtained  from  the  fact  that 
the  two  wave  systems,  in  order  that  they  should  pro- 


PHENOMENA   OF  INTERFERENCE.  221 

duce  dark  lines  in  the  given  points  of  the  screen,  must 
proceed  simultaneously,  and  in  a  precisely  similar 
manner,  from  the  two  luminous  points.  But  we  are 
unable  so  to  conduct  the  process  of  light  production  in 
two  luminous  bodies,  or  even  in  two  points  of  a  single 
luminous  body,  as  to  make  the  undulating  movement 
proceeding  from  one  exactly  accordant  with  that  of  the 
other ;  in  each  of  them,  after  a  short  period,  interrup- 
tion of  the  movement,  augmentation  and  diminution  of 
the  liveliness  of  the  flame,  and  other  disturbances  take 
place,  which  do  not  occur  coincidently  in  the  other. 
Hence  the  lines  of  interference  are  only  partially 
formed,  and  in  rapidly  changing  parts  of  the  screen 
giving  to  the  eye  the  impression  that  it  is  equally  and 
uniformly  illuminated.  Two  independent  and  separate 
luminous  points  therefore,  on  account  of  the  inequality 
of  these  wave  systems,  present  no  interference  lines. 
The  equality  required  for  this  purpose  is  obtained  with 
the  greatest  certainty  by  making  the  two  wave  systems 
spring  by  mirrors  or  by  any  other  appropriate  means 
from  the  same  source.  The  irregularities  to  which  the 
process  of  light  production  is  subjected,  whatever  may 
be  the  light  used,  take  place  concordantly  and  simulta- 
neously in  both  systems  of  waves,  and  consequently 
exercise  no  influence  upon  the  accordance  and  opposi- 
vtion  of  the  rays  which  are  now  conditioned  only  by 
I  their  difference  of  path. 

94.  Fresnel's  experiment  may  now  be  repeated, 
with  this  difference,  that  a  red  and  a  blue  glass  are 
placed  alternately  before  the  aperture  of  the  Heliostat. 
It  is  then  seen  that  with  blue  light  the  lines  are  closer 
together  than  in  the  red,  that  is  to  say,  the  correspond- 
in<r  series  of  dark  lines  are  in  the  former  case  nearer  to 


222  OPTICS. 

the  middle  bright  lines  than  in  the  latter.  Two  blue 
rays  thus  require,  in  order  that  they  may  neutralise 
each  other,  a  smaller  linear  difference  than  two  red 
ones  ;  the  wave-length  of  Hue  light  is  consequently  smaller 
than  of  red  light. 

If  as  brilliant  a  spectrum  as  possible  be  produced 
by  means  of  a  prism,  and  its  coloured  rays  be  allowed 
to  fall  successively  upon  the  lens  L  (fig.  134),  and  con- 
sequently on  the  mirror,  we  find  that  the  distance 
between  the  lines,  and  consequently  the  wave-lengths, 
become  progressively  smaller  in  passing  from  the  red  to 
the  violet.  This  affords  an  explanation  of  the  reason 
why,  when  white  light  is  employed,  the  lines  are  not 
alternately  black  and  white,  but  coloured.  The  middle 
bright  lines,  in  which  all  colours  are  mingled  in  their 
highest  intensity,  are  completely  white,  but  towards 
the  sides  first  the  violet  fades  out,  and  then  in  succes- 
sion the  several  colours  from  the  most  towards  the 
least  refrangible.  The  consequence  of  this  is  that  the 
middle  bright  lines  towards  the  interior  are  edged  with 
yellow,  and  towards  the  exterior  with  red  ;  at  the  point 
where  the  brightest  colour,  yellow,  disappears,  the  first 
dark  line  is  seen,  which,  however,  since  the  violet  has 
here  again  become  stronger,  exhibits  a  faint  violet  tint. 
Then  follow  white,  yellowish-red,  violet,  to  the  second 
dark  line,  -which  is  blue.  Then  come  green,  yellow, 
red,  bluish-green  ;  still  further  on  a  few  alternations  of 
red  and  bluish-green  occur,  and  very  soon,  inasmuch 
as  the  lines  of  various  colours  mingle,  only  a  uniform 
white  remains.  White  light  therefore  gives  only  a  few 
lines,  which  as  we  pass  outwards  constantly  become  more 
and  more  indistinct ;  when  homogeneous  light  is  used, 


OF  THE 

I  UNIVERSITY 

PHENOMENA   OF  INTERFERENCE.     \ 


un  the  other  hand,  the  dark  lines  are  completely 
and  are  present  in  great  numbers. 

FiesnePs  experiment,  however,  not  only  shows 
broadly  that  there  are  differences  in  the  lengths  of  the 
waves,  but  it  enables  us  to  measure  these  differences. 

If,  for  example,  the  length  of  the  rays  proceeding 
from  the  luminous  points  towards  the  first  black  lines 
be  obtained,  which  can  be  done  with  sufficient  accuracy, 
their  difference  must  be  equal  to  half  the  wave-lengths 
of  the  homogeneous  light  employed.  In  the  lines  of 
higher  order  which  correspond  to  the  differences  of 
path  of  3,  5,  7,  etc.  half  wave-lengths,  the  measure- 
ment can  be  repeated  with  the  accuracy  required. 
Fresnel  made  these  measurements  for  light  which  had 
traversed  red  glass,  and  found  the  wave-length  of  this 
red  light  equal  to  638  millionths  of  a  millimeter. 

A  method  will  hereafter  be  shown  by  which  the 
wave-lengths  may  be  determined  with  still  greater 
accuracy  and  for  definite  rays  (for  the  Fraunhofer's 
lines).  A  conception  of  the  extraordinary  smallness 
of  the  waves  of  light  may  be  obtained  from  the  state- 
ment that  in  the  length  of  one  millimeter  there  are 
1,315  waves  of  the  extreme  red  (line  A),  1,698  waves  of 
the  yellow  light  of  Sodium  (line  D),  and  2,542  waves 
of  the  extreme  violet  (line  H2}. 

95.  It  is  well  known  that  if  the  performance  of  a  piece 
of  music  be  listened  to  at  various  distances,  the  same 
accordance  in  the  notes,  the  same  harmony,  is  always 
perceived  ;  the  high  and  the  deep  notes  which  fall  in 
the  same  beat  reach  our  ears  in  all  cases  simultaneously. 
The  conclusion  from  this  is  that  all  tones,  whether  high 
or  low,  strong  or  feeble,  are  propagated  through  the  air 
with  equal  rapidity.  The  rapidity  of  propagation  ol 
16 


224  OPTICS. 

sound,  that  is,  the  distance  to  which  the  vibratory 
movement  of  a  resounding  body  spreads  in  the  air  in 
a  second,  is  estimated  at  340  metres  (1115*4  feet). 

But,  as  has  been  already  shown,  a  complete  wave 
originates  with  each  entire  vibration  ;  every  sounding 
body  will  therefore  produce  as  many  successive  sound 
waves  in  a  second  as  the  number  of  its  vibrations  in  a 
second,  and  since  the  sound  in  this  period  of  time  has 
spread  over  a.  distance  of  340  metres,  the  total  length 
of  the  sound  waves  excited  in  one  second  must  amount 
to  340  metres.  The  wave-length  of  a  tone  is  conse- 
quently obtained  by  dividing  the  rapidity  of  propaga- 
tion (340m.)  by  the  number  of  its  vibrations.  The 
wave-length  of  the  tone  of  an  A  tuning  fork,  which 
makes  440  vibrations  in  a  second,  is  thus  found  to  be 
equal  to  773  millimeters.  The  wave-length  of  every 
movement  the  rapidity  of  propagation  of  which  is 
known  to  us,  may  in  this  way  be  deduced  from  the 
number  of  vibrations,  and  of  course  also,  conversely, 
from  the  wave-length  the  number  of  vibrations. 

The  rapidity  of  propagation  of  light  is  so  enormously 
great  that  even  at  a  distance  of  60  miles,  which  is  as 
far  as  terrestrial  signals  will  reach,  no  difference  of 
time  can  be  observed  between  the  moment  of  emission 
and  of  arrival.  The  velocity  of  light  has,  however, 
jbeen  measured  by  means  of  astronomical  observations, 
land  more  recently  by  physical  experiments.  An 
account  of  the  ingenious  methods  by  which  this  has 
been  accomplished  cannot  be  here  appropriately  in- 
troduced. It  is  only  requisite  to  state  that  the  concor- 
dant results  of  all  measurements  show  that  the  light 
both  of  celestial  bodies  as  well  as  that  proceeding  from 
terrestrial  sources,  traverses  a  distance  of  about  186,000 


PHENOMENA  OF  INTERFERENCE.  225 

miles  a  second.     Some  observations  by  Arago,*  and  espe- 
cially also  reasons  which  are  theoretically  deduced  from 
the  nature  of  undulatory  movements,  justify  us  in  admit- 
ting that  the  rapidity   of  propagation  of  every  kind  of  \ 
light,  whatever  may  be  its  colour  and  brightness,  is,  in  the  \ 
free  cether  of  the  universe,  alike. 

The  wave-lengths  of  the  homogeneous  kinds  of 
light,  as  well  as  their  rapidity  of  propagation,  being 
now  known,  the  number  of  their  vibrations  can  be 
determined  with  facility.  This  is  expressed  by  the 
number  of  wave-lengths  which  are  contained  in  the 
length  of  186,000  miles.  The  extreme  red  line  (^4), 
1,315  of  the  waves  of  which  occur  in  a  millimeter, 
are  thus  found  to  have  the  prodigious  number  of 
394,500000,000000,  or  in  round  numbers,  395  billions 
-of  vibrations  in  a  second.  The  shorter  the  wave-lengili 
the  greater  must  be  the  number  of  vibrations ;  in  a  ray 
of  yellow  Sodium  light  every  particle  of  aether  makes 
509  billions  of  vibrations  in  a  second,  and  the  extreme 
violet  line  (H2)  corresponds  to  a  number  of  vibrations 
amounting  to  763  billions. 

A  musical  note  appears  to  our  ears  higher  in  pitch, 
the  greater  the  number  of  its  vibrations  in  a  given  time  ; 
and  just  as  the  ear  perceives  the  rapidity  of  the  vibra- 

*  If  light  of  different  colours  travelled  with  different  velocity,  a  white 
star  which  became  suddenly  visible  would  be  seen  by  an  observer  at  a  dis- 
tance of  that  colour  in  the  first  instance  which  propagates  itself  with  the 
greatest  velocity,  and  then  of  a  succession  of  mixed  colours  till  it  by  degrees 
became  white.  If  it  then  again  disappeared  it  would  pass  through  a  similar 
.  series  of  colours  in  inverse  order  till  it  dissolved  into  the  slowest- moving 
colour.  Similar  phenomena  would  be  exhibited  by  the  variable  stars,  espe- 
cially if  their  period  were  short,  and  there  were  a  considerable  difference 
between  their  greatest  and  least  brightness.  Arago  undertook  a  series  of 
observations  in  regard  to  Algol  in  Perseus,  which  fulfils  these  conditions, 
but  could  perceive  no  change  of  colour. 


226  OPTICS. 

tions  of  sound  as  pitch  of  sound,  so  does  the  eye  per- 
ceive the  frequency  of  the  undulations  of  light  as  colour. 
Thus  for  the  sensation  of  yellow  characterising1  the 
Sodium  flame  to  be  produced  in  our  minds  509  billions 
of  sether,  neither  more  nor  less,  must  enter  the  eye 
and  strike  the  retina.  Speaking  generally,  the  colour  oj 
\  every  homogeneous  ray  of  light  is  determined  exclusively 
j  by  the  number  of  its  vibrations  ;  the  number  of  vibrations 
is  the  objective  characteristic  of  that  which  we  perceive 
subjectively  as  colour.  The  succession  of  colours  in 
the  spectrum  is  consequently  to  be  regarded  as  a  scale 
which  rises  from  the  lowest  tone  perceptible  to  our  eye, 
the  extreme  red,  to  the  highest,  the  extreme  violet. 
Antecedent  to  the  commencement  of  the  visible  scale 
in  the  red,  are  the  deeper  ultra-red  tones,  the  vibrations 
of  which  are  too  slow  to  excite  the  sensation  of  light 
in  our  optic  nerves,  and  at  the  other  extremity  are  to 
be  added  on  as  highest  tones  the  ultra-violet  which  pro- 
duce only  an  extremely  feeble  impression  of  light  in 
our  eyes. 

96.  It  is  now  requisite  that  close  attention  should 
be  paid  to  a  chain  of  reasoning  that  will  here  be  offered 
in  regard  to  a  few  experiments  of  the  simplest  kind. 

A  close  wound  spiral  coil  which  hangs  vertically  in 
front  of  a  scale  divided  into  centimeters  carries  at 
its  lower  end  a  plain  brass  ball.  The  lowest  part  of  the 
ball  has  a  little  hook.  On  attaching  to  this  a  weight 
of  100  grammes  the  elastic  coil  at  once  becomes  elon- 
gated and  the  brass  ball  descends  two  centimeters.  With 
a  weight  of  200  grammes  the  elongation  is  twice  as 
much,  or  four  centimeters,  and  three  times  the  weight 
again  produces  three  times  the  amount  of  elongation. 

Thus  it  appears  that  the  force  which  must  be  applied 


PHENOMENA   OF   INTERFERENCE.  227 

to  move  the  ball  from  its  original  position  in  opposi- 
tion to  the  elasticity  of  the  wire  increases  in  the  same 
ratio  as  the  amount  of  displacement  effected. 

Let  the  weights  be  now  removed  and  when  the  ball 
has  returned  to  its  original  position,  let  it  be  pressed  down 
with  the  fingers  about  two  centimeters  ;  then  inasmuch 
as  it  is  kept  in  this  position,  the  pressure  downwards 
exerted  must  be  identical  with  the  weight  of  100 
grammes,  which  was  before  necessary  to  effect  this 
elongation,  and  when  the  ball  is  set  free  it  returns  with 
this  force  to  its  position  of  equilibrium. 

When,  however,  it  has  reached  the  position  of  equi- 
librium it  does  not  at  once  come  to  rest,  but  continues 
to  perform  upward  and  downward  movements  which 
are  slow  enough  to  permit  them  to  be  counted.  If  the 
ball  be  now  depressed  to  the  extent  of  4  centimeters, 
and  then  be  set  at  liberty,  it  has  twice  as  far  to  go  from 
its  extreme  point  to  the  position  of  equilibrium,  or 
the  extent  (or  amplitude)  of  its  vibration  is  now  doubled. 
If  its  vibrations  are  now  counted  the  same  number  of 
vibrations  will  be  found  as  in  the  former  case,  for  since 
not  only  the  space  traversed  but  also  the  expression  of 
force  of  the  tense  spiral  wire  has  now  been  doubled, 
the  greater  space  must  be  traversed  in  the  same 
time.  Nor  is  any  alteration  observable  in  the  number 
of  vibrations  when  the  ball  is  drawn  down  to  the  extent 
of  6  centimeters  from  its  position  of  rest,  although  the 
amplitude  of  its  vibration  is  increased  threefold. 

From  this  it  appears  that  the  number  of  vibrations 
is  dependent  exclusively  upon  the  nature  of  the  vibrat- 
ing body — upon  its  internal  forces,  if  we  may  so  speak, 
— but  in  no  way  upon  the  amount  of  the  external  force 
applied  to  it;  the  amount  of  force  applied  to  it  finds  ita 


228  OPTICS. 

expression  in  the  amplitude  of  the  vibration.  When  the 
ball  is  depressed  four  centimeters,  the  hand  has  not  only 
to  exercise  twice  as  much  force,  but  it  has  to  traverse 
twice  the  distance  that  it  has  when  it  is  only  depressed 
two  centimeters.  The  ivork  which  must  be  performed 
to  overcome  the  elastic  force  of  the  wire  in  the  former 
case  is  therefore  four  times  as  great  as  in  the  latter, 
and  if  with  three  times  the  force  the  ball  be  moved  over 
three  times  the  space,  nine  times  the  amount  of  force 
used  in  the  first  instance  has  to  be  applied.  When  the 
hand  is  removed  the  work  performed  by  it  is  transferred 
to  the  ball,  and  expresses  itself  in  the  energy  of  its 
vibrating  movements.  By  virtue  of  this  energy  the 
ball,  until  it  comes  to  rest,  performs  the  same  amount  ot 
work  which  was  applied  to  it  to  set  it  in  movement. 

From  these  considerations  it  results  that  the  energy 
of  the  vibrating  movement  is  proportional  to  the  square 
of  the  amplitude  of  the  vibrations. 

The  facts  taught  by  the  vibrating  ball  are  applicable 
alike  to  the  vibrations  of  sound  and  of  light.  The  tint 
of  colour  is  dependent  on  the  frequency  ;  the  intensity  (or 
energy)  of  light  on  the  liveliness  of  the  vibrations.  Whilst 
the  former  depend  on  the  number  of  the  vibrations,  the 
latter  are  measured  by  the  square  of  the  amplitude  oi 
the  vibrations. 


HUYGHENS'   PRINCIPLE.  229 


CHAPTER  XVII. 


97.  f  LIGHT  consists  of  a  very  minute  vibrating  move- 
ment of  an  elastic  medium,  which  is  propagated  with 
great  rapidity,  but  not  instantaneously,  in  straight 
lines  that  proceed  like  the  radii  of  a  sphere  from  a 
central  point  common  to  all.' 

Hooke,*  the  accomplished  friend  and  countryman 
of  Newton,  who  wrote  the  date  1(564  under  these  words, 
may  be  regarded  as  the  first  who  clearly  seized  and 
/  expressed  the  fundamental  idea  of  the  doctrine  of 
luminous  waves.  Nevertheless  he  did  not  advance  so 
far  as  to  explain  the  refraction  of  light  by  undulatory 
movement;  and  he  failed  because  this  fundamental 
idea,  in  order  to  be  applicable  to  all  the  phenomena  of 
light,  required  still  a  very  important  addition  to  com- 
plete and  perfect  it.  It  was  reserved  for  Hooke's  genial 
contemporary,  Huyghens,t  to  fill  this  hiatus,  and  to 
become  the  real  founder  of  the  undulatory  theory  off. 
light. 

The  theory  of  Huyghens,  so  named  to  do  honour  to 
its  discoverer,  is  in  fact  the  egg  of  Columbus,  a  simple 
solution  of  many  complex  and  enigmatical  phenomena, 
and  whilst  an  attempt  is  here  made  to  render  it  intel- 

*  Micrographia,  Observat.  ix. 
f   Tractatus  de  Lumine,  1690. 


230 


OPTICS. 


Huyghens'  principle. 


ligible,  no  very  great  strain  will  be  exerted  on  ordinary 
powers  of  imagination.  When  an  undulatory  move- 
ment propagates  itself  through  an 
elastic  medium,  every  particle  imi- 
tates the  movement  of  the  particle 
first  excited.  Bat  every  particle 
stands  in  regard  to  the  adjoining 
ones  in  exactly  the  same  relation 
that  the  first  particle  did  to  its 
neighbours,  and  consequently  must 
exert  upon  those  that  surround 
it  exactly  the  same  influence  as 
the  first.  Every  vibrating  particle 
is  therefore  to  be  regarded  as  if  it  were 
the  originally  excited  particle  of  a 
ivave  system ;  and  as  the  innumerable 
and  simultaneous  '  elementary '  wave  systems  co-operate 
with  one  another  at  each  instant  in  accordance  with  the  prin- 
ciple of  interference,  we  obtain  exactly  that  'principal 
wave  system  '  by  which  the  elastic  medium  appears  at  any 
moment  to  be  moved. 

If,  for  example,  all  points  of  the  circular  or  spheri- 
cal wave  B  C  (fig.  137)  which  take  origin  from  the 
centre  of  disturbance  A  be  regarded  as  new  centres  of 
disturbance,  after  a  little  while  an  innumerable  series 
of  elementary  waves  of  equal  size  will  have  formed 
around  them,  which  are  represented  in  the  figure  by 
small  arcs.  The  circle  B'  Gf  described  around  the 
centre  A,  which  all  the  elementary  waves  touch  at  their 
most  distant  point,  represents  the  extreme  limits  to 
which  the  undulatory  movement  has  in  the  meanwhile 
been  propagated.  The  state  of  oscillation  which  pre- 
viously affected  the  wave  B  C  is  now  transferred  to  the 


HUYGHENS'  PKINCIPLE.  231 

circle  Bf  C",  to  wliich  all  elementary  waves  reach  with 
equal  conditions  of  oscillation.  The  wave  B  G  has  thua 
propagated  itself  by  means  of  the  elementary  waves  in 
the  same  form  and  with  the  same  rapidity  to  B'  0",  as 
if  it  proceeded  directly  from  the  original  point  of  dis- 
turbance A. 

The  same  result  is  thus  obtained  whether  we  admit 
a  direct  propagation  of  a  single  wave  centre  outwards, 
or  an  indirect  propagation  effected  by  innumerable 
elementary  waves.  Nevertheless  the  two  modes  of 
'explanation  are  essentially  different,  and  the  latter  is 
alone  true  to  nature,  for  it  alone  gives  the  requisite 
consideration  to.  the  various  relations  that  occur  between 
the  particles  of  an  elastic  medium.  The  former  more 
simple  mode  of  explanation  may,  however,  be  admitted 
if,  as  in  the  preceding  Cha.pter,  we  are  dealing  with 
those  characters  of  wave  movement  which  are  common 
to  both  methods  of  propagation.  /  As  long  as  a  wave 
movement  is  propagated  without  disturbance,  the  ele- 
mentary waves  withdraw  themselves  from  observation 
because  they  proceed  by  their  co-operation  to  produce  the 
chief  waves.  They  immediately  appear  independently, 
however,  if  their  adjoining  waves  are  in  any  way  sup- 
pressed. If,  for  example  (in  fig.  137),  the  wave  BO 
proceeding  from  A  passes  through  the  opening  B  C  of  a 
screen,  it  continues  its  course  undisturbed  between  the 
two  marginal  rays  A  B  and  A  0,  whilst  the  elementary 
waves  proceeding  from  their  points  between  B  and  C 
combine  in  the  manner  above  described  to  form  the 
chief  wave  B'  C'.  The  elementary  waves  B'  b  and 
(7  c  proceeding  from  the  marginal  points  B  and  C 
remain  partially  isolated,  and  transfer  a  movement 
which,  in  comparison  with  the  main  wave,  is,  as  may  be 


232  OPTICS. 

supposed,  very  feeble,  into  those  lateral  spaces  Br  B  8 
and  (7(7  8,  which  are  protected  from  the  main  wave. 

Phenomena  of  light  will  soon  be  referred  to  which 
are  caused  by  a  similar  lateral  expansion  of  elementary 
waves.  Some  further  consideration  must  however  still 
be  given  to  the  behaviour  of  the  principal  wave. 

98.  The  chief  wave  proceeding  from  the  combined 
action  of  the  elementary  waves  spreads  itself,  as  has 
been  seen,  around  a  luminous  point  in  a  concave  sphere 
just  as  if  the  propagation  took  place  directly  from  this 
point.  Both  modes  of  explanation  permit  us  equally  to 
explain  the  movement  of  light  as  a  rectilinear  radiation ' 
from  a  centre.  Careful  consideration  however  shows 
that  there  is  an  essential  difference  between  the  two 
views.  Whilst,  on  the  older  theory,  a  direct  propagation 
along  a  single  straight  line,  that  is,  the  possibility  of 
an  isolated  ray  of  light,  was  accepted;  on  the  other 
theory  in  view  of  the  action  which  every  particle  of 
sether  exercises  upon  the  adjoining  ones,  the  existence  of 
an  isolated  ray  of  light  is  inconceivable. 

Nevertheless  a  ray  of  light  may  be  conceived  as 
the  expression  of  the  direction  in  which  the  small 
portion  of  wave  belonging  to  it  lying  upon  the  surface 
of  the  sphere  is  propagated.  Speaking  generally,  the 
wave  itself  or  parts  of  the  same,  must  constantly  be  kept 
in  view  if  it  be  desired  to  draw  any  conclusions  on  the 
laws  of  the  phenomena  of  light. 

However  small  a  portion  of  the  wave  surface  may 
be  represented,  it  contains  innumerable  rays,  which 
collectively  form  a  6eam,  or  fasciculus  of  rays  (Strah- 
lenbiindel).  In  point  of  fact,  in  optical  experiments 
individual  rays  of  light  are  never  dealt  with,  but  always 
beams. 


HUYGHENS'   PRINCIPLE.  233 

The  statements  formerly  made  on  the  supposition  of 
the  existence  of  Individ ual  rays  of  light,  however, 
lose  none  of  their  force  through  the  different  concep- 
tion just  gained.  They  still  remain  perfectly  accurate, 
even  when  each  'ray  of  light'  is  regarded  as  only 
the  representative  of  the  very  thin  beam  to  which 
it  belongs. 

In  free  sether,  as  well  as  generally  in  every  medium 
in  which  the  undulations  of  light  propagate  themselves 
spherically  with  equal  velocity,  every  ray  is  a  radius 
perpendicular  to  the  wave  segment  corresponding  to 
it.  If  we  imagine  the  wave  segment  to  be  very  small 
or  very  remote  from  the  centre  of  the  sphere,  the 
perpendicular  rays  falling  upon  it  may  be  regarded  as 
parallel  to  each  other,  and  the  wave  segments  themselves 
as  plane.  Speaking  generally,  every  fasciculus  of 
parallel  rays  is  propagated  by  plane  waves  which  are 
perpendicular  to  the  direction  of  the  radiation. 

99.  Now  that  by  means  of  Huyghens'  theory  we 
have  given  an  explanation  of  the  real  mechanism  of 
undulatory  movement,  we  shall  proceed  to  inquire  what 
happens  when  a  wave  of  light  reaches  the  plane  surface 
of  junction  of  two  different  media,  as  for  example  a 
surface  of  water  at  rest. 

In  fig.  138  a  b  represents  a  plane  portion  of  an 
undulation,  and  A  aBb'  the  parallel  fasciculus  of  rays 
corresponding  to  it.  As  the  wave  moves  onwards  towards 
the  surface  M  N,  the  particles  of  aether  between  a  and  b' 
gradually  become  affected  by  the  movement;  every 
point  struck  becomes,  in  accordance  with  the  theory  oi 
Huyghens,  itself  a  centre  of  disturbance,  and  sends 
forth  an  elementary  wave  into  the  first  medium  (the  air) 
as  well  as  into  the  second. 


234 


OPTICS. 


Let  us  now  consider  in  the  next  place  the  elementary 
waves  returning  into  the  first  medium. 

At  the  instant  at  which  the  point  V  is  reached  by  the 
undulatory  movement,  an  elementary  wave  has  formed 
around  the  point  originally  disturbed,  a,  the  radius 
of  which  must  be  equal  to  the  line  b  b' ',  to  which  extent 
the  chief  or  principal  wave  has  in  the  meanwhile  pro- 
gressed ;  this  elementary  wave  is  indicated  in  the  figure 
at  c  by  an  arc  described  from  the  point  a.  In  like  manner 
the  points  lying  between  a  and  V  have  produced  ele- 


FIG.  138. 


Explanation  of  reflexion  and  refraction. 

mentary  waves  the  radii  of  which  are  smaller  in  propor- 
tion as  they  are  nearer  to  the  point  ¥  which  is  still  at 
rest.  If  from  V  the  tangent  V  c  be  drawn  to  the  first 
elementary  wave,  it  touches  also  all  the  other  elementary 
waves,  and  consequently  represents  the  principal  wave 
which  results  from  the  co-operation  of  all  the  elemen- 
tary waves.  This  wave  b'  c,  which  is  reflected  in  the 
direction  of  the  fasciculus  aCfe'Dinto  the  first  medium, 
forms  with  M  N  the  angle  c  b'a,  which  is  obviously  equal 
to  the  angle  b  a  V  of  the  '  incident '  wave.  If  at  a  upon 
the  limiting  plane  MN  the  perpendicular  a  /,  the  '  per- 
pendicular of  incidence/  be  raised,  the  angle  A  a  I,  which 


HUYGHENS'   PKINCIPLR.  235 

the  incident  ray  A  a  forms  with  the  same,  is  equal  to  the 
angle  b  a V  which  the  wave  corresponding  to  it  forms  with 
M  N9  and  the  same  holds  good  for  the  reflected  raj  a  C. 
The  angle  of  reflexion  is  thus  always  equal  to  the  angle  oj 
incidence.  We  see  therefore  that  the  law  of  reflexion 
is  a  necessary  consequence  of  the  undulatory  theory. 

But  elementary  waves  also  penetrate  into  the  second 
medium  from  the  point  of  the  surface  disturbed,  though 
the  rapidity  of  propagation  is  different  from  that  in  the 
first  medium.  The  elementary  wave  proceeding  from 
the  point  a  must  therefore  at  the  instant  in  which  the 
incident  wave  reaches  the  point  V,  possess  a  radius  a  e 
which  stands  in  the  same  relation  to  the  radius  a  c 
( =  bb')  of  the  wave  reflected  from  this  point  into  the 
first  medium,  that  the  rapidity  of  propagation  of  the 
light  in  the  second  does  to  that  in  the  first  medium. 
In  the  figure  a  c  is  smaller  than  b  &',  that  is,  the 
rapidity  in  the  second  medium  is  taken  as  being 
smaller  than  in  the  first.  As  the  tangent  b'  e  drawn 
from  b'  to  this  first  elementary  wave  touches  also 
all  the  other  hitherto  formed  elementary  waves,  and 
consequently  includes  these  movements  in  itself,  it 
represents  the  plane  principal  wave  penetrating  into 
the  second  medium.  The  direction  of  the  fasciculus 
aEb'F  corresponding  to  it  is  given  by  the  line  a  e, 
which  is  drawn  from  a  towards  the  point  of  contact  E. 
It  is  now  plain  that  the  ray  a  E  forms  an  angle  r  with 
the  perpendicular  a  I',  which  differs  from  the  angle  oi 
incidence  i,  and  in  our  case  is  smaller  than  this.  The 
ray  A  a  has  consequently  experienced  a  deflection  from 
the  perpendicular  in  its  passage  from  the  first  into  the 
second  medium.  The  refracted  wave  b'  e  forms  the 
angle  r  with  the  surface  M N. 


236  OPTICS. 

If  the  particular  line  here  shown,  a  &',  be  now  taken 
as  unity,  b  I/  is  the  sine  of  the  angle  of  incidence  i,  and 
a  e  the  sine  of  the  angle  of  refraction  r.  The  length  of 
the  line  b  V  stands  in  the  same  ratio  to  that  of  a  e 
as  the  rapidity  of  the  propagation  of  light  in  the  first  to 
that  in  the  second  medium.  This  relation  is  invariable, 
whatever  may  be  the  magnitude  of  the  angle  of  incidence. 
We  thus  arrive  at  the  proposition  that 

The  sine  of  the  angle  of  incidence  holds  an  invariable 
and  unalterable  ratio  to  the  angle  of  refraction. 

The  foregoing  statements  have,  however,  not  only 
shown  that  the  law  of  refraction  is  a  necessary  conse- 
quence of  the  uiidulatory  theory,  but  they  also  supply  a 
key  to  the  proper  signification  of  this  unchangeable 
proportion  which  we  have  hitherto  designated  as  the 
'  index  of  refraction.'  The  index  of  refraction  in  the  pas- 
sage of  light  from  one  medium  into  another  must  be  equal 
to  the  relation  that  the  rapidity  of  propagation  of  light  in 
the  first  medium  bears  to  its  rapidity  in  the  second. 

As  the  index  of  refraction  from  air  into  water  is 
equal  to  -J,  the  velocity  of  light  in  air  as  compared  with 
water  must  be  as  4  :  3.  If  in  the  former  it  amount  to 
300,000  kilometers  (186,414  miles),  it  must  be  one- 
fourth  less  in  water,  namely  225,000  kilometers  (139,810 
miles).  Speaking  generally,  it  is  a  necessary  conse- 
quence of  the  undulatory  theory,  that  light  is  propagated 
more  slowly  through  strongly  refracting  than  in  feebbj 
refracting  media. 

It  is  necessary  here  to  revert  for  a  moment  to  the 
view,  that  light  is  a  peculiar  kind  of  matter,  notwith- 
standing that  this  view  has  been  on  good  grounds  set 
aside.  On  this  view  refraction  is  explained  by  supposing 
that  the  particles  of  the  refracting  medium  exert  an  at- 


HUYGHENS'  PRINCIPLE.  237 

traction  or  influence  upon  the  particles  of  the  supposed 
luminous  substance,  and  the  conclusion  is  arrived  at 
that  light  pi'opagates  itself  more  rapidly  in  the  strongly 
refracting  medium  than  in  the  feebler  one.  The  direct 
contradiction  which  is  presented  by  these  opposite  con- 
clusions affords  an  opportunity  of  finally  settling  the 
long  contest  between  the  material  and  undulatory 
theories  of  light.  Foucault  has  shown  by  means  of  very 
ingenious  experiments  that  light  does  travel  more  slowly 
in  water  than  in  air.  If  therefore  the  reasons -formerly 
adduced  should  still  be  considered  to  leave  any  doubt  in 
regard  to  the  nature  of  light,  there  can  now  be  no  ques- 
tion that  the  undulatory  theory  must  be  regarded  as 
the  only  true  theory  of  light. 

100.  Before  proceeding  further  an  attempt  must 
be  made  to  remove  another  doubt  which  might  arise 
in  regard  to  the  considerations  from  which  the  law 
of  reflexion,  as  well  as  that  of  refraction,  have  fol- 
lowed. It  might  be  objected,  namely,  that  these  con- 
siderations should  be  applicable  if  the  same  substance 
existed  below  the  limiting  surface  M  N  as  above;  and 
that  we  should  then  obtain  instead  of  the  refracted  ray, 
the  rectilinear  continuation  of  the  incident,  but  also 
always  reflected  ray. 

Since  now  in  this  case  the  position  of  the  plane 
M  N  could  be  imagined  anywhere,  it  would  result,  in 
opposition  to  facts,  that  in  a  medium  of  uniform 
nature  light  could  not  only  propagate  itself  forwards 
from  the  source  of  light,  but  also  from  all  points  back- 
wards, and  consequently  even  backwards  against  the 
source  of  light. 

That  the  rapidity  of  propagation  of  light  in  a  re- 
fracting medium  is  smaller  than  in  the  surrounding 


238 


OPTICS. 


Fm.  139. 


air  may  be  explained  on  the  not  improbable  assumption 
that  the  sether  contained  in  a  solid  or  fluid  body  pos- 
sesses a  greater  density  than  that  contained  in  the  air, 
or  the  free  sether  of  space. 

In  order  to  give  some  idea  of  what  happens  when 
an  undulatory  movement  arrives  at  the  limiting  line  of 
two  media  of  dissimilar  density,  an  analogy  may  be 
employed.  If  two  ivory  balls  (fig.  139)  be  taken,  of 
unequal  size,  hanging  by  threads  and  in  contact  with 
each  other,  and  the  smaller  ball  be  raised  and  allowed  to 
fall  against  the  larger,  the  latter  is  set  in  motion  in  the 
direction  of  the  blow ;  the  smaller 
one,  on  the  contrary,  rebounds  and 
moves  in  the  opposite  direction 
to  that  which  it  originally  had. 
After  both  balls  have  again  come 
to  rest,  if  the  larger  ball  be  raised 
and  allowed  to  strike  the  smaller 
one,  it  will  be  seen  that  whilst 
this  is  driven  forwards  the  former 
still  moves,  though  more  slowly, 
forwards.  In  both  cases  then  the 
striking  ball,  after  it  has  parted  with  a  portion  of  its 
motion,  still  continues  to  move. 

Not  so  if  two  balls  of  equal  size  (fig.  139)  be 
made  to  strike  one  another.  The  striking  ball  now 
remains  at  rest  whilst  it  transfers  the  whole  of  its 
motion  to  the  ball  struck,  compelling  this  to  move 
onwards. 

The  transference  of  motion  from  a  vibrating  layer  of 
sether  to  a  quiescent  one,  i.e.,  the  propagation  of  light,  is 
performed  under  precisely  similar  laws.  If  both  layers 
are  of  equal  density,  and  hence  of  equal  mass,  the 


Impact  of  elastic  balls. 


HUYGHENS'  PKINCIPLE.  239 

second  acquires  the  entire  motion  of  the  first,  which 
itself  remains  at  rest  until  it  again  receives  a  new 
impulse  from  behind,  that  is  to  say,  from  the  source  of 
light.  In  one  and  the  same  medium  therefore  no 
backward-moving  elementary  waves  can  arise.  But  if 
the  density,  and  consequently  the  mass,  of  the  aether 
layer  struck  be  greater  or  smaller  than  that  of  the 
striking  layer,  the  latter  retains  a  portion  of  its  motion 
and  gives  rise  to  those  backward-going  elementary 
waves  which  combine  to  form  a  reflected  principal  wave. 
From  this  it  is  seen  that  reflexion  can  only  occur  at 
the  limiting  surface  of  two  layers  of  aether  of  unequal 
density. 

101.  The  experiment  with  unequal  balls  attracts 
attention  to  another  circumstance  which  accompanies 
the  reflexion  of  luminous  waves,  namely,  that  the 
striking  ball  maintains  the  direction  of  its  movement, 
or  the  reverse  direction,  according  to  whether  its  mass 
is  greater  or  smaller  than  that  of  the  ball  struck.  In  like 
manner  the  undulatory  motion  which  is  retained  by  the 
last  layer  of  the  first  medium  and  produces  the  reflected 
wave,  moves  in  the  same  or  in  the  opposite  direction  to 
the  movement  of  the  incident  ray,  according  to  whether 
the  first  medium  is  more  or  less  dense  than  the  second. 
In  reflexion  at  a  denser  medium  the  undulations  of 
the  reflected  ray  are  directly  opposite  to  those  which 
it  would  make  were  it  the  immediate  continuation  of 
the  corresponding  incident  ray.  But  we  now  know 
that  in  any  ray,  those  particles  that  are  distant  from 
each  other  a  half  wave-length  are  in  opposite  conditions 
of  movement.  If  we  therefore  imagine  the  wave  line 
(fig.  135)  to  be  pushed  back  half  a  wave-length,  the 
motion  of  all  the  particles  becomes  reversed.  The 
17 


240  OPTICS. 

result  previously  obtained  may  therefore  be  expressed 
in  the  following  way  : — 

In  reflexion  at  the  surface  of  a  denser  medium  the 
reflected  ray  undergoes  a  retardation  in  respect  to  the 
incident  ray  of  a  half  wave-length.  In  reflexion  at  the 
surface  of  a  less  dense  medium,  on  the  other  hand,  no 
such  retardation  occurs. 

102.  The  velocity  of  light  being  smaller  in  a  re- 
fracting medium  than  in  air,  a  ray  of  light  traversing 
a  glass  plate,  for  example,  must  experience  a  retardation 
in  comparison  with  a  ray  of  light  which  has  travelled 
the  same  distance  in  air,  and  this  retardation  will  be 
greater  in  proportion  to  the  thickness  of  glass  tra- 
versed. 

If  we  apply  this  consideration  to  the  rays  which 
emanating  from  a  luminous  point  strike  upon  a  convex 
lens  and  unite  on  the  other  side  into  a  focus,  it  may 
appear  at  first  sight  as  if,  because  they  have  to  traverse 
very  different  paths,  they  must  strike  it  with  very 
different  velocities.  But  it  is  not  so.  They  arrive  at 
the  focal  point  with  equal  conditions  of  undulation  just 
as  if  they  had  all  traversed  the  same  path.  If  we 
compare  any  given  lateral  ray  with  the  axial  ray,  the 
former  has  indeed  a  longer  path  to  traverse  in  the  air, 
but  a  consequently  less  thickness  of  glass ;  and  a  more 
exact  examination  shows  that  the  greater  retardation 
which  it  experiences  in  the  air  is  completely  com 
pensated  for  by  the  smaller  retardation  in  the  glass. 

A  lens  therefore  produces  no  difference  of  velocity  in 
the  several  rays  of  a  fasciculus,  inasmuch  as  it  unites  them 
in  a  (real  or  virtual)  focus,  and  allows  those  differences 
which  were  originally  present  to  remain  unaltered. 

This  is  the  reason  why    we   observe   the   lines   of 


HUYGHENS'  THE011Y. 

Fresnel  and  other  phenomena  of  interference  subjec- 
tively, that  is  to  say,  through  the  eye  (which  is  indeed 
nothing  but  an  apparatus  of  lenses)  either  with  or 
without  a  lens  or  telescope,  without  any  disturbance 
of  the  phenomenon  through  the  action  of  the  lens. 


242  OPTICS. 


CHAPTER  XVIII. 

DISPERSION    OF    LIGHT.       ABSORPTION. 

103.  AFTER  having  acquired  a  knowledge  of  the  true 
significance  of  the  index  of  refraction  as  the  relation  of 
velocity  of  propagation  in  the  first  to  that  in  the  second 
medium,  it  is  easy  to  express  the  facts  of  the  dispersion 
of  colour  in  the  language  of  the  undulatory  theory. 
To  say  that  waves  of  different  colour  undergo  an  un- 
equal amount  of  refraction  is  equivalent  to  stating 
that  in  a  colour-dispersing  medium  the  various  homo- 
'geneous  kinds  of  light  are  propagated  with  different 
velocities. 

The  proposition,  that  all  kinds  of  light  are  propagated 
with  equal  rapidity,  which  we  were  formerly  compelled 
to  admit  in  regard  to  the  free  aether  of  the  universe,  is 
thus  no  longer  admissible  for  the  aether  contained  in 
the  interior  and  occupying  the  interstices  of  the  particles 
of  natural  substances. 

The  action  which  the  particles  of  a  body  exert  upon 
the  undulations  of  aether  propagating  themselves  in  it, 
may  be  conceived  to  be  dependent  on  the  nature  of 
these  particles.  In  very  many  fluids  and  solids,  espe- 
cially in  the  colourless  and  transparent  ones,  as  water, 
glass,  &c..  the  rays  produced  by  more  rapid  undulations 
are  n  ore  strongly  deflected,  that  is  to  say,  experience 


EISPEKSION   OF  LIGHT.      ABSOEPTION.  243 

a  greater  amount  of  retardation  than  the  rays  produced 
by  a  smaller  number  of  undulations.  Prisms  composed 
of  such  substances  exhibit  a  spectrum  with  the  ordinary 
succession  of  colours,  from  the  least  refrangible  red  to 
the  most  refrangible  violet  rays.  The  specific  nature 
of  the  substance  is  however  rendered  evident  even  here 
by  the  different  arrangement  of  the  lines  of  Fraunhofer. 
(See  fig.  106.) 

The  dispersion  of  colour  in  atmospheric  air  and 
in  gaseous  bodies  generally  is  (according  to  Ketteler) 
so  insignificant  that  we  may  admit  in  them,  as  in 
free  aether,  equal  velocity  for  all  kinds  of  light,  being 
smaller  than  that  of  universal  space  in  the  proportion 
of  1  :  1-000294.  This  number  expresses  the  index  of  re- 
fraction of  a  ray  of  light  in  its  passage  from  empty  space, 
that  is  to  say,  space  filled  with  free  aether  alone,  into 
air  at  a  temperature  of  0°  C.  and  under  760  millimeters 
pressure. 

The  influence  of  the  nature  of  the  material  par- 
ticles on  the  velocity  of  propagation  is  remarkably 

FIG.  140. 


Unusual  dispersion  power  of  Fuchsin. 


exhibited  in  coloured  substances,  especially  in  those  in 
whose  absorption  spectra  one  or  more  very  dark  lines 
appear.  If  we  introduce,  for  example,  an  alcoholic 


244  OPTICS. 

solution  of  the  anilin  colour  '  Fuchsin  '  into  a  hollow 
prism  (fig.  53)  and  look  through  it  at  a  brightly  illumi- 
nated slit,  we  obtain  a  spectrum  in  which  blue  and 
violet  are  less  deflected  than  yellow  and  red.  •  What  is 
elsewhere  the  end  of  the  spectrum  here  appears  at 
the  commencement,  towards  the  middle  it  fades,  and 
in  the  centre  the  green,  being  absorbed,  is  absent  (fig. 
140).  From  this  behaviour  the  conclusion  may  be 
drawn  that  in  Fuchsin  the  blue  and  violet  rays  are 
propagated  with  greater  velocity  than  the  red  and 
yellow. 

This  phenomenon,  which  was  discovered  by  Chris- 
tiansen, and  was  shown  by  Kundt  to  be  presented  by  a 
great  number  of  absorbing  substances,  has  been  called 
anomalous  dispersion  of  light. 

104.  The  phenomena  of  anomalous  dispersion 
renders  us  strongly  disposed  to  the  opinion  that  neither 
the  refrangibility  nor  the  length  of  undulation,  but  the 
number  of  vibrations,  is  to  be  regarded  as  the  character- 
istic of  a  homogeneous  ray  of  light.  The  number  of 
undulations  by  which  the  impression  of  colour  perceived 
by  our  eyes  is  conditioned  does  not  undergo  any  altera- 
tion in  the  passage  of  light  from  one  medium  into  another. 
In  fact  we  observe  no  change  of  tint  (Tonhohe)  when, 
for  example,  the  yellow  light  of  Sodium  passes  from  air 
into  water. 

The  length  of  the  waves,  however,  does  undergo  a  change. 
The  wave  length  is,  it  is  to  be  remembered,  always 
obtained  by  dividing  the  velocity  of  propagation  by 
the  number  of  vibrations.  As  the  latter  remains  un- 
changed, whilst  the  velocity  of  propagation  in  water  is 
only  three-fourths  of  the  velocity  in  air,  the  wave- 
leiicrth  in  water  can  onlv  amount  to  three-fourths  of 


DISPERSION   OF  LIGHT.     ABSORPTION.  245 

the  wave-length  in  air.  The  wave-Length  of  a  ray  of 
light  in  any  given  substance  is  consequently  obtained  by 
dividing  the  wave-length  in  air  by  the  index  of  refraction 
of  the  substance  itself. 

105.  We  possess  no  means  of  changing  the  number 
of  vibrations,  that  is  to  say,  the  colour  of  a  homo- 
geneous ray  of  light.  But  that  such  an  alteration  may 
and  does  occur  under  certain  circumstances  may  now 
be  demonstrated. 

The  sensation  of  a  definite  colour  is  conditioned  by 
the  number  of  waves  of  aether  that  penetrate  into  the 
eye  in  a  second,  just  as  the  pitch  of  a  musical  note 
depends  on  the  number  of  waves  of  sound  which  enter 
the  ear  in  the  same  space  of  time.  As  long  ago  as 
1841  Doppler  called  attention  to  the  fact  that  the  pitch 
of  a  musical  note  or  the  colour  of  an  impression  of  light 
mast  be  raised  or  lowered  when  the  resounding  or 
luminous  body  approximates  or  recedes  from  the 
observer.  In  the  former  case  the  organ  of  sense  is 
struck  in  the  course  of  a  second  by  a  greater,  in  the 
latter  case  by  a  less,  number  of  waves  than  if  the  source 
of  light  or  sound  be  stationary.  As  regards  sound  the 
truth  of  the  principle  of  Doppler  can  easily  be  demon- 
strated by  experiment ;  it  is  only  necessary  to  allude 
to  what  may  perhaps  have  been  noticed  by  many. 
During  the  passage  of  a  train  through  a  station  it  may 
be  observed  that  the  whistle  of  a  locomotive  becomes 
higher  in  pitch  as  it  approximates  to,  and  lower  in  pitch 
as  it  recedes  from  the  observer  than  when  it  is  at  rest. 
It  is  impossible,  no  doubt,  to  make  a  similar  experiment 
in  the  case  of  light,  because  the  greatest  velocity  we 
can  attain  is  vanishingly  small  in  comparison  with  its 
enormous  speed.  Nevertheless  the  possibility  of  its 


246  OPTICS. 

occurrence  in  the  case  of  the  waves  of  light  cannot 
be  doubted. 

Let  it  be  conceived  that  in  free  space  a  sphere  of 
glowing  Sodium  vapour  is  moving  with  sufficient  velo- 
city towards  our  earth,  its  light  would  appear  more  green 
than  that  of  a  terrestrial  Sodium  flame,  whilst  if  it 
were  receding  it  would  assume  a  reddish  tint.  And  if 
this  light  fell  upon  a  prism  instead  of  our  eye  it  would 
reach  the  prism  in  the  former  case  with  a  greater  and 
in  the  latter  case  with  a  smaller  number  of  undulations 
than  that  of  a  Sodium  flame  at  rest,  and  in  correspon- 
dence with  this  would  experience  a  stronger  or  weaker 
deflection.  Hence  it  follows  that  if  a  spectroscope  be 
directed  towards  the  moving  source  of  light  the  bright 
Sodium  line  would  appear  to  have  changed  its  position 
and  to  be  advanced  towards  the  more,  or  towards  the 
less  refrangible  end  of  the  spectrum,  according  as  the 
source  of  light  was  approximated  to,  or  made  to  recede 
from  the  observer. 

Just  as  the  bright  Sodium  line  in  this  example 
undergoes  a  change  of  position,  so  also,  when  the  fixed 
star  moves  in  the  direction  of  the  visual  line  with 
sufficient  velocity,  do  the  dark  lines  in  the  spectrum  of 
a  fixed  star  become  altered  and  no  longer  coincide  with 
the  bright  lines  of  the  elementary  substances  to  the 
absorbing  action  of  which  they  owe  their  origin.  From 
the  direction  and  amount  of  this  dislocation  both  the 
direction  and  the  velocity  of  the  movement  of  the  star 
can  be  deduced. 

106.  Huggins,  on  comparing  the  F  line  of  the 
spectrum  of  Sirius  with  the  blue-green  line  of  the 
spectrum  of  a  Geissler's  tube  filled  with  hydrogen, 
found  the  former  as  compared  with  the  latter  moved 


DISPERSION   OF  LIGHT.      ABSORPTION.  247 

towards  the  red,  and  to  an  extent  that  if  the  wave- 
length of  the  Hydrogen  line  F  is  486*5  millionths  of  a 
millimeter,  the  wave-length  of  the  line  of  Sirius  corre- 
sponding to  it  was  about  0*109  millionth  of  a  millimeter 
greater.1^  Hence  it  appears  that  at  the  time  of  observa- 
tion Sirius  was  receding  from  the  earth  with  a  velocity 
which,  compared  with  that  of  light  (300,000)  is  as 
0-109  is  to  486-5.  The  velocity  with  which  the  two 
celestial  bodies  receded  from  each  other  was  con- 
sequently 

300,000  .  0-109 

' - =  o7  kilometers  =  41i  miles. 

486*0 

Since  at  the  time  of  the  observation  the  earth  was 
moving  away  from  Sirius  at  the  rate  of  19  kilometers 
(nearly  12  miles)  in  each  second,  there  remains  a  surplus 
48  kilometers  (about  30  miles),  which  represents  the  rate 
at  which  Sirius  was  receding  from  our  solar  system. 

Observations  made  with  the  telescope  long  ago 
taught  astronomers  that  many  fixed  stars  possess  a 
proper  motion  of  their  own.  But  it  is  obvious  that  by 
means  of  the  telescope  only  that  portion  of  the  motion 
can  be  recognised  which  takes  place  at  right  angles 
to  the  visual  line.  The  spectroscope,  on  the  other 
hand,  indicates  to  us  the  movement  which  escapes  tele- 
scopic observation,  that  namely  which  takes  place  in  the 
visual  line.  It  is  thus  apparent  that  by  combining  the 
results  of  different  methods  of  investigation  it  is  possible 
to  determine  the  true  motion  of  the  fixed  stars  in  space. 

The  conclusion  may  be  drawn  from  the  rapid  change 
of  form  which  is  observable  in  the  solar  protuberances 
that  the  glowing  masses  of  hydrogen  of  which  they 
consist  are  in  the  most  violent  motion.  Peculiar  dis- 


248  OPTICS. 

locations  and  disturbances,  which  Lockjer  has  observed 
in  the  dark  F  line  of  the  solar  spectrum  as  well  as  in 
the. bright  F  line  of  the  photosphere,  have  enabled  him 
to  measure  with  precision  the  velocity  with  which  the 
glowing  hydrogen  streams  up  in  the  solar  atmosphere 
or  revolves  in  whorls  of  storm. 

The  alteration  in  the  number  of  undulations  which 
corresponds  to  these  dislocations  shows  that  a  rapidity 
of  from  50  to  60  kilometers  per  second  is  nothing 
unusual,  indeed  the  most  marked  dislocation  hitherto 
observed  indicates  a  velocity  of  190  kilometers  (nearly 
120  miles).  If  we  compare  these  fearfully  violent  hydro- 
gen storms  in  the  solar  atmosphere  with  even  the  most 
violent  hurricanes  of  our  atmosphere,  which  at  most  do 
not  exceed  45  meters  (W50  feet)  per  second,  these  last 
appear  to  be  only  gentle  breathings. 

107.  We  have  hitherto  regarded  the  process  of  the 
propagation  of  light  from  the  standpoint  of  the  un- 
dulatory  theory.  It  remains  to  consider  the  origin  of 
light,  that  is  to  say,  the  process  of  illumination,  from 
the  same  point  of  view.  The  analogy  of  light  to  sound, 
which  has  so  often  afforded  us  useful  hints,  will  also  aid 
materially  in  this  part  of  the  subject. 

A  mass  of  matter  becomes  a  source  of  heat  and 
light  in  consequence  of  an  extremely  rapid  vibrating 
movement  of  its  smallest  particles,  which  is  propagated 
as  a  series  of  undulations  into  the  surrounding  aether, 
and  is  felt  by  our  tactile  nerves  as  heat,  but  by  our 
optic  nerves,  if  the  undulations  are  sufficiently  rapid, 
as  light. 

Certain  facts  which  especially  belong  to  the  domain 
of  Chemistry  lead  to  the  conclusion  that  the  matter  of 
which  bodies  are  composed  does  not  entirely  fil]  the 


DISPEKSION   OF  LIGHT.      ABSORPTION.  249 

space  it  occupies,  but  consists  of  separate  particles 
which,  in  a  physical  sense,  are  no  further  divisible,  and 
are  therefore  termed  ultimate  particles  or  atoms.  The 
interspaces  of  the  atoms  are  filled  with  aether. 

There  are  as  many  different  kinds  of  atoms  as  there 
are  elementary  chemical  bodies.  Chemistry  teaches  us 
further  that  the  atoms  in  any  substance,  even  in  an 
element,  never  occur  singly,  but  are  always  united  by 
the  action  of  chemical  affinity  to  form  groups  of  two 
or  more  atoms.  Such  a  group  of  atoms  is  called  a 
molecule.  Every  molecule  is  built  up  by  its  atoms  in 
a  perfectly  definite  manner.  The  kind,  number,  and 
grouping  of  the  atoms  which  compose  a  molecule 
determine  the  chemical  qualities  of  the  molecule,  and 
consequently  also  of  the  substance,  which  consists  of  an 
indefinite  number  of  such  similar  molecules. 

And  just  as  a  cliord  gives  a  definite  fundamental 
note  besides  its  overtones,  dependent  on  the  length, 
thickness,  tension,  and  consistence  of  the  ci^ord,  so  also 
the  atoms  within  every  molecule  are  capable  of  only 
a  definite  series  of  vibrations,  the  number  of  vibrations 
being  determined  by  the  structure  of  the  molecule,  that 
is  to  say,  by  its  chemical  properties.  And  just  as  it  may 
be  said  that  a  chord  or  tuning  fork  is  tuned  to  give  a 
particular  note,  it  may  also  be  said  that  a  Sodium  mole- 
cule is  tuned  to  the  colour-tone  D. 

It  may  hence  be  imagined  that  the  chemical  nature 
of  a  body  must  betray  itself  by  characteristic  bright 
lines  in  the  spectrum  of  its  light. 

Whilst  the  chemical  properties  of  a  body  are  deter- 
mined by  the  internal  structure  of  its  molecules,  its 
physical  properties,  especially  its  condition  of  aggrega- 
tion (whether  it  be  solid,  fluid,  or  gaseous)  depends 


250  OPTICS. 

upon  the  special  mode  in  which  its  molecules  are 
arranged  amongst  themselves. 

In  a  solid  body  the  molecules  are  held  together, 
in  determinate  positions  of  equilibrium  around  which 
they  can  vibrate,  by  a  powerful  force,  which  is  termed 
the  force  of  cohesion  (Zusammenhangkraft).  These 
vibrations  are  independent  of  the  peculiar  quality  of  the 
molecules ;  they  include  also  some  vibrations  of  a  less 
known  character,  but  take  place  with  all  possible  num- 
bers of  vibrations,  and  for  all  solid  bodies  in  a  similar 
manner  at  the  same  temperatures. 

Solid  bodies  therefore,  whatever  may  be  their 
chemical  nature,  give  alike  a  continuous  spectrum,  which 
at  a  lower  temperature  only  contains  the  invisible 
ultra-red  rays ;  as  the  temperature  rises  not  only  does 
the  strength  of  the  ladiation  increase,  but  a  higher 
tone  of  colour  is  constantly  being  superadded  to 
that  previously  presort.  At  about  540°  C.  the  red 
shows  itself  as  fir  ns  T>  (dark  red  glow,  dull  or  low  red 
heat)  ;  at  about  700°  C.  (bright  or  cherry-red  heat)  the 
spectrum  extends  to  the  farther  side  of  F ;  and  lastly, 
at  white  heat  (1200°  C.)  it  reaches  to  H.  Glowing 
fluids,  between  the  molecules  of  which  the  force  oi 
cohesion  still  acts,  exhibit  a  continuous  spectrum. 
These  vibrations  which  the  molecules  of  solid  and 
fluid  bodies  exhibit  under  the  influences  of  the  force 
of  cohesion,  do  not  prevent  the  simultaneous  occurrence 
of  those  vibrations  within  each  molecule  tc  which  the 
molecule  is  attuned  owing  to  its  chemical  composition, 
As  a  general  rule*  the  latter  are  not  visible,  because 

*  According  to  Bahr  and  Bunsen  the  fixed  oxides  of  Erbium  and  Didj- 
mium,  when  heated  to  glowing,  exhibit  a  spectrum  with  bright  lines  which 
correspond  to  the  dark  striae  in  their  absorption  spectra.  (See  §  75.) 


DISPERSION   OF   LIGHT.      ABSORPTION.  251 

the  bright  lines  which  correspond  to  them  disappear 
upon  the  bright  background  of  the  continuous  spectrum. 
The  characteristic  linear  spectrum  which  discloses  to 
us  the  chemical  quality  of  a  body  is  much  better  and 
more  clearly  seen  when  its  molecules,  freed  from  the 
chains  of  cohesion,  enter  into  the  gaseous  condition. 

108.  Fig.  141  represents  a  tuning  fork  fixed  into  a 
little  wooden  box  open  at  one  FIG  ui 

end,  and  when  made  to  vi- 
brate it  is  heard  to  give  a 
pure  soft  tone.  A  second 
tuning  fork  similarly  sup- 
ported on  a  box  is  placed 
beside  it.  If  now  the  first 
be  made  to  vibrate  and  be 
then  immediately  silenced  by 
touching1  it  with  the  finger, 

Tuning  fork. 

the    second   one,    which  was 

previously  at  rest,  will  be  heard  resounding  with  the 
samo  note.  It  has  been  set  into  vibration  by  the  waves 
of  air  which  proceeded  from  the  first. 

But  if  the  second  fork  be  put  out  of  tune  by  attach- 
ing a  little  piece  of  wax  to  its  arms,  and  the  experiment 
be  repeated,  it  remains  perfectly  silent.  The  resonance 
thus  only  occurs  when  the  two  forks  are  in  unison  with 
each  other,  that  is,  when  the  second  possesses  the  same 
number  of  vibrations  as  the  undulations  of  air  proceed- 
ing from  the  first. 

A  similar  phenomenon  is  familiarly  known  to  all. 
If  a  person  sings  into  an  open  piano  with  a  loud  voice 
the  same  note-  is  gently  returned  in  answer ;  those 
c'hprds  namely,  which  when  struck  by  their  hammers 
yield  this  note,  are  set  in  vibration  by  the  sound,  but 


252  OPTICS. 

the  waves  of  sound  excited  by  the  singer  pass  over  all 
the  other  chords  without  acting  011  them. 

This  vibration  in  unison  which  is  called  forth  by 
tones  of  equal  height,  and  is  termed  resonance,  may  be 
.  easily  explained.  Every  wave  of  sound  which  reaches 
the  tuning  fork  begins  to  set  it  in  movement.  If  the 
impulses  of  the  waves  succeed  to  each  other  in  the 
same  time  as  the  vibrations  of  which  the  tuning  fork 
is  capable,  each  arm  of  the  fork  when  it  is  about  to 
move  forwards  will  receive  an  impulse  forwards,  and 
when  it  moves  backwards  an  impulse  backwards.  The 
succeeding  impulses  thus  act  unopposed  to  strengthen 
the  movement  which  was  only  feebly  commenced  by 
the  first,  and  soon  excite  the  fork  to  lively  vibration. 
If,  on  the  contrary,  the  number  of  vibrations  of  the 
waves  differs  from  that  of  the  fork,  the  later  impulses 
very  soon  come  to  be  in  opposition  to  the  slight  tremb- 
ling excited  by  the  first,  and  neutralise  their  action. 
The  tuning  fork  therefore  remains  at  rest.  To  set  the 
tuning  fork  in  motion  the  unisonal  waves  must  give  up 
a  part  of  the  energy  of  their  motion  to  it ;  they  there- 
fore proceed  in  a  weakened  condition  on  the  other  side 
of  the  fork.  The  waves  not  in  unison,  on  the  other 
hand,  give  off  none  of  their  energy  to  the  tuning  fork, 
but  pass  by  it  of  their  original  strength. 

If  now  a  large  number  of  tuning  forks  be  imagined 
to  be  attached  to  a  table,  and  a  sound  Avave  unisonal 
with  them  be  excited  at  one  end,  it  will  reach  the  other 
in  a  very  weakened  condition,  because  its  energy  will 
ha^e  been  in  great  measure  absorbed  by  the  tuning 
forks  A  wave  of  another  pitch  will,  on  the  contrary, 
traverse  the  layer  of  tuning  forks  almost  unaltered, 
and  will  spread  beyond  them  without  noticeable  loss. 


DISPERSION   OF  LIGHT.      ABSORPTION.  253 

A  Bun  sen's  flame  in  which  float  glowing  particles 
of  Sodium  is  comparable  to  such  a  layer  of  tuning 
forks,  and  it  is  now  intelligible  why  the  peculiar  kind 
of  light,  D,  which  it  emits,  is  weakened  or  altogether 
vanishes  in  traversing  it,  whilst  it  remains  transparent 
for  all  other  kinds  of  light. 

The  nndulatory  theory  thus  aifords  an  explanatioo 
of  absorption,  inasmuch  as  it  shows  that  every  body 
must  absorb  exactly  those  kinds  of  luminous  rays  which 
it  is  itself  capable  of  emitting. 

109.  Although  a  wave  vanishes  by  absorption,  the 
energy  of  its  movement  is  by  no  means  suppressed,  but 
is  transferred  without  loss  to  the  absorbing  body.  For 
in  accordance  with  the  fundamental  law  of  all  natural 
phenomena,  the  principle  of  the  conservation  of  energy, 
energy  can  as  little  be  destroyed  as  created. 

The  motor  energy  which  is  transferred  to  the  ab- 
sorbing body  may  become  manifest  in  this  in  two 
forms ;  a  clock  can  obviously  be  set  and  kept  in  motion 
if  the  axis  of  the  great  wheel  be  turned.  In  this  case 
the  active  energy  of  the  hand  is  transferred  into  the 
active  energy  of  the  clockwork  in  motion.  A  watch 
may  also  be  made  to  go  by  winding  it  up,  that  is  to 
say,  by  coiling  an  elastic  spring  around  the  main  wheel. 
The  active  energy  of  the  hand  is  now  transferred  to  the 
wound-up  spring,  and  remains  slumbering  in  it  as 
inactive  energy.,  or  energy  of  tension,  as  long  as  the 
movement  of  the  clockwork  is  checked.  But  as  soon 
as  the  detent  is  loosed,  however  long  a  period  may 
elapse,  the  spring  gradually  uncoils  itself  to  its  pre- 
viously unstrained  condition,  and  thus  the  whole 
energy  which  had  been  concealed  in  it  in  an  inactive 


254  OPTICS. 

state  again  makes  its  appearance  as  the  active  energy 
of  the  clockwork  in  motion. 

Let  this  simile  be  applied  to  the  absorption  of  the 
Eether  waves.  A  portion  of  the  active  energy  of  the 
absorbed  wave  sets  the  molecules,  and  the  atoms  within 
the  molecules,  in  motion,  or  renders  the  motion  already 
present  in  them  more  lively.  They  become  themselves 
by  this  means  the  centre  of  waves  of  aether,  the  active 
energy  of  which  betrays  itself  to  our  senses  as  heat  or 
light  (glowing  phosphorescence  and  fluorescence). 

Another  portion  of  the  energy  absorbed  is  employed 
in  loosening  or  altogether  dissolving  the  chains  which 
bind  the  molecules  together  to  form  a  substance,  or  the 
atoms  together  to  form  a  molecule.  When  the  mole- 
cules of  the  body,  or  the  atoms  within  each  molecule, 
are  widely  separated  from  each  other  or  are  completely 
dissociated,  ihe  body  becomes  extended,  and  passes  from 
the  solid  into  the  fluid  or  gaseous  condition;  or  lastly, 
it  experiences,  if  the  molecules  split  into  their  atoms,  a 
chemical  decomposition.  In  the  former  physical,  as  in 
the  latter  chemical  action,  a  portion  of  the  absorbed 
energy  is  consumed  in  overcoming  the  molecular  forces 
(force  of  cohesion  and  of  chemical  affinity),  just  as  the 
energy  of  the  hand  applied  in  winding  up  the  watch  is 
used  to  overcome  the  elastic  force  of  the  spring.  The 
energy  so  applied,  is,  however,  by  no  means  lost,  but 
remains  stored  up  in  the  body  or  in  its  particles  as 
energy  of  tension  as  long  as  the  body  remains  in  iis 
condition  of  solution  or  division.  It  makes  its  appear- 
ance im  mediately  again  as  active  energy,  in  its  original 
amount,  if  the  body  revert  from  its  new  into  its  old 
condition. 

110.  The   various   operations    which   the   radiation 


DISPERSION   OF  LIGHT.      ABSORPTION.  255 

from  the  sun  can  produce  ou  the  surface  of  our  earth 
may  serve  to  illustrate  these  statements.  Were  the 
sun's  rays  completely  reflected  from  the  surface  of  the 
earth  they  could  neither  warm  nor  in  any  other  way  act 
upon  it ;  their  action  is  only  rendered  possible  by  the 
absorbing  action  of  terrestrial  objects. 

The  transparent  air  allows  the  sun's  rays  to  traverse 
it  almost  undiminished  in  intensity,  and  is  therefore  to 
only  a  very  slight  extent  directly  warmed  by  it.  On  the 
other  hand,  the  solid  crust  of  the  earth,  which  possesses 
considerable  absorptive  power,  undergoes  a  great  amount 
of  heating ;  th«  air  itself  becomes  gradually  warmed  from 
the  soil ;  and  since  this  heating  takes  place  unequally 
at  different  parts  of  the  earth's  surface,  attaining  for 
example  a  higher  degree  in  the  equatorial  than  in  the 
polar  regions,  the  equilibrium  of  the  atmosphere  is 
disturbed,  and  seeks  restoration  by  currents  which  we 
call  winds.  The  movements  of  our  atmosphere  are 
thus  primarily  caused  by  the  sun's  rays ;  in  the  breeze 
which  swells  the  sails  of  the  ship,  as  in  the  hurricane 
which  uproots  trees,  a  part  of  the  energy  is  made  mani- 
fest which  the  sun  sent  down  to  the  globe  of  the  earth 
in  the  form  of  aether  waves. 

The  evaporation  which  takes  place  from  the  surface 
of  the  sea  under  the  influence  of  the  solar  rays  causes 
the  ascent  of  extraordinary  quantities  of  aqueous 
vapour  into  the  higher  regions  of  the  atmosphere,  from 
whence,  again  condensed,  they  descend,  in  the  form  of 
water  or  of  snow,  and  collected  into  streams  and  rivers, 
flow  back  to  the  sea.  In  performing  this  circuit  the 
water  gives  off  the  whole  of  the  energy  which  it 
originally  received  from  the  sun.  The  falling  drops  of 
rain,  the  ship-bearing  river,  the  waterfall  which  turns 
18 


256  OPTICS. 

the  mill-wheel  or  drives  the  tunnel-K  rer  through,  the 

o 

granite  of  the  Alps,  owe  their  energy  to  the  sun. 

In  the  green  leaves  of  plants  the  carbonic  acid  they 
have  absorbed  from  the  air  undergoes  decomposition 
by  the  absorbed  solar  rays,  and  the  oxygen  returns  to 
the  air  in  a  gaseous  form,  whilst  the  carbon  is  applied  to 
the  construction  of  the  solid  parts  of  the  plant.  In  the 
wood  of  the  stem  of  a  tree  the  whole  energy  of  the 
solar  rays  which  has  been  consumed  in  its  formation  in 
the  course  of  years  is  found  stored  up  in  an  inactive 
condition  ;  it  reappears  with  undiminished  intensity  as 
active  energy  in  the  form  of  light  and  heat  when  the 
wood,  or  rather  the  carbon  contained  in  it,  again  reverts 
by  the  process  of  combustion  to  the  condition  of  car- 
bonic acid.  The  Carboniferous  strata,  which  are  com- 
posed of  the  altered  remains  of  ancient  plants,  represent 
a  highly  economical  mass  of  solar  energy  which,  after 
a  slumber  lasting  for  ages,  is  again  set  free  by  the  pro- 
cess of  combustion,  heating  and  illuminating  our  houses, 
striking  the  hammers  and  turning  the  spindles  in  our 
workshops,  and  driving  our  locomotives  with  the  speed 
of  the  wind  along  their  iron  paths. 

Amongst  the  animal  creation  some  feed  directly  on 
vegetables,  whilst  others  consume  their  plant-eating 
congeners.  In  both  instances  we  recognise  the  vege- 
table world  as  the  only  spring  of  all  animal  life.  In 
the  animal  organism  the  carbon  consumed  as  food 
unites  with  the  inspired  oxygen,  and  is  exhaled  in  the 
form  of  carbonic  acid.  The  force  condensed  in  the 
vegetable  streams  forth  again  in  the  animal  body  ;  that 
is  to  say,  the  energy  of  the  solar  rays  which  the  plant 
required  for  the  separation  of  the  carbon  is  again  set 
free  in  the  animal  body  as  heat  and  motion.  The  heat 


DISPERSION   OF  LIGHT.      ABSORPTION.  257 

of  the  blood,  the  motion  of  our  heart,  the  capacity  for 
work  in  our  arms,  all  represent  the  energy  which 
originally  streamed  from  the  sun.  Thus  the  sun,  by 
means  of  the  waves  which  it  excites  in  the  aether  ocean 
of  the  universe,  is  the  origin  of  all  the  heat,  life,  and 
motion  on  the  surface  of  our  earth.* 

*  There  are  no  doubt  a  few  terrestrial  movements  which  are  not  oc- 
casioned by  the  radiation  from  the  sun ;  such,  for  instance,  as  the  ebb  and 
flow  of  the  tides,  which  are  caused  by  the  force  of  attraction  of  the  moon 
and  sun  upon  the  waters  of  the  sea.  So  also  volcanic  activity  which  has 
its  origin  in  the  interior  of  the  earth.  Lastly,  there  are  stores  of  energy  of 
tension  which  do  not  depend  upon  the  sun,  which  are  stored  up  in  certain 
combustible  minerals  (in  virgin  sulphur,  iron,  &c.).  Nevertheless,  all  these 
sources  of  force  together  are  very  insignificant  in  comparison  with  those 
which  are  supplied  to  us  by  th 


258  OPTICS. 


CHAPTEE    XIX. 

DIFFRACTION    OF    LIGHT. 

111.  THE  last  four  Chapters  having  been  occupied  in 
rendering  the  facts  stated  in  the  earlier  section  of  this 
work  intelligible  on  the  undulatory  theory,  we  may  now 
enter  upon  the  consideration  of  new  phenomena  of  light 
adapted  to  support  the  views  already  expressed,  and  to 
supply  additional  means  of  determining  the  essential 
nature  of  light. 

If  a  beam  of  parallel  solar  rays  be  allowed  to  fall 
upon  a  narrow  vertical  slit,  and  the  transmitted  light  be 
received  upon  a  paper  screen  at  some  distance  from  it, 
FIG  U2  there  is  seen  on  either  side 

of  the  bright  line  which 
naturally  results  from  the 
shape  of  the  slit,  a  series 
of  alternate  dark  and  light 
strise  (fig.  142),  which 

Diffraction  or  inflection  image  of  a  narrow    rapidly   diminish    in   inten- 

slit-  sity  as  they  are  more  dis- 

tant from  the  central  line,  and  are  fringed  with  the 
same  subdued  colours  that  have  already  been  seen  in 
the  interference  lines  of  Fresnel. 

This  experiment  furnishes  the  practical  proof  that 
light  spreads  not  simply  in  straight  lines,  but,  as  Huy- 
ghens'  construction  shows,  laterally  also.  It  is,  in  fact, 


DIFFRACTION  OF  LIGHT.  259 

simply  the  realisation  of  the  case  already  mentioned 
(§  97),  that  a  wave  in  its  passage  through  an  opening, 
whilst  it  is  propagated  directly  as  a  principal  wave,  also 
fcends  forth  elementary  waves  into  the  space  which  is 
protected  from  the  chief  wave. 

The  white  line  in  the  middle  is  that  part  of  the 
screen  which  receives  the  principal  waves,  that  is  to  say, 
here  all  the  elementary  waves  or  elementary  rays  pro- 
ceeding from  the  various  points  of  the  aperture  are  found 
in  unison,  and  support  each  other  in  the  most  complete 
manner.  The  elementary  waves  uniting  in  a  laterally 
situated  point  of  the  screen — called  diffracted  rays — 
are  not  capable  of  an  equally  favourable  co-operation, 
since,  proceeding  from  the  various  points  of  the  aperture 
they  travel  over  various  paths  to  the  screen,  and  become 
according  to  the  difference  of  their  path,  i.e.,  according 
to  the  distance  of  the  point  of  the  screen  observed  from 
the  middle  stria,  sometimes  in  partial  accordance,  some- 
times in  complete  discordance,  and  thus  are  produced 
alternately  the  bright  and  dark  striae  observed  upon  the 
screen.  This  phenomenon,  because  it  originates  by  the 
interference  of  inflected  rays,  is  termed  a  phenomenon  of 
diffraction.  When  monochromatic  light  is  used,  the  dark 
lines  appear  of  a  deep  black  colour,  and  are  closer  to 
each  other,  as  well  as  to  the  central  bright  line,  in 
proportion  as  the  wave-lengths  of  the  source  of  light 
employed  are  smaller.  With  white  light,  therefore,  only 
the  central  stria  appears  white,  whilst  the  lateral  striae 
appear,  for  the  same  reason  and  in  the  same  order, 
coloured,  like  the  interference  striae  of  Fresnel. 

If  the  slit  be  gradually  widened  the  lines  will  be 
seen  to  become  progressively  narrower,  till  they  ulti- 


260 


OPTICS. 


FIG.  143. 


mately  become  so  fine  as  to  be  no  longer  perceptible.  In 
order  therefore  to  perceive  the  laterally  spreading 
elementary  waves,  very  narrow  slits  alone  can  be  used ; 
with  wide  apertures  they  are  undoubtedly  present,  but 
the  phenomena  of  diffraction  are  then  so  extremely 
delicate  that  they  escape  observation. 

112.    The   phenomena  of   diffraction   may  also  be 
seen  with  the  naked  eye,  if  a  distant  object  be  looked 

at  through  a  minute  aper- 
ture. They  may  be  still 
fl  more  advantageously  ob- 
served by  employing  a 
U  telescope,  at  the  objective 
end  of  which  (A,  fig.  143) 
a  tube  (B),  lined  with 
leather,  is  attached  for  the  Deception  of  the  wooden 
ring,  c.  A  sheet  of  tin  is  let  into  the  latter,  in 
which  is  a  small  opening,  d.  The  diffraction  figures 
which  then  come  into  view  present  various  forms, 


Diffraction  apparatus. 


FIG.  14. 


FIG. 145. 


Phenomena  of  diffraction  with  a  circular 
aperture. 


Phenomena  of  diffraction  with  a 
rhomboidal  aperture. 


according  to  the  shape  of  the  opening,  and  are  often 
of  surprising  delicacy.  Amongst  the  most  simple  is 
the  figure  which  is  obtained  from  a  circular  aperture 
(fig.  144).  In  this  case  a  .bright  circular  disc  ap- 
pears, surrounded  by  a  succession  of  bright  and  dark 
rings,  which,  when  white  light  is  used,  are  fringed 


DIFFRACTION   OF  LIGHT.  261 

with  delicate  colours.  With  a  rhomboidal  figure  (o,  fig. 
145)  the  image  is  divided  by  two  rows  of  dark  lines, 
each  of  which  is  parallel  to  the  sides  of  the  opening, 
into  numerous  parallelograms.  The  most  distinct  of 
these,  which  are  arranged  serially  at  the  four  sides, 
give  to  the  image  the  aspect  of  an  oblique  cross  artifi- 
cially constructed  in  mosaic  work. 

When  a  telescope  is  used  for  the  purpose  of 
observing  the  diffraction  image,  it  is  formed  in  the 
focal  plane  of  the  objective,  and  is  seen  magnified 
through  the  ocular.  The  telescope  permits  conse- 
quently of  the  application  of  wider,  and  therefore  of 
more  strongly  illuminated  apertures,  the  diffraction 
Bgures  of  which  would  be  too  small  to  be  seen  by  the 
naked  eye. 

113.  It  has  already  been  pointed  out  how  the  pheno- 
mena of  diffraction  result  from  the  interference  of  the  ele- 
mentary rays.  It  may  now  be  advisable  to  enter  a  little 
more  deeply  into  an  explanation  of  them,  under  the 
supposition  that  they  are  being  observed  writh  a  tele- 
scope, or  even  with  the  naked  eye. 

In  fig.  146,  AB  represents  the  horizontal  section  of 
a  screen,  and  C  and  D  the  edges  of  a  vertical  slit  which 
has  been  made  in  it.  If  a  fasciculus  of  parallel  homo- 
geneous rays,  c  G  d  D  fall  vertically  upon  the  screen, 
all  fether  particles  within  CD  are  in  equal  conditions  of 
undulation.  From  each  of  them,  in  accordance  with 
Huyghens'  principle,  elementary  rays  spread  in  all 
possible  directions.  All  the  rays  which  proceed  from 
the  various  points  of  the  aperture  parallel  to  each 
other  are  united  in  one  point  of  its  focal  plane  by  the 
objective.  The  fasciculus  of  diffracted  rays,  CEDF, 
for  example,  which  forms  the  angle  of  diffraction  (f>  with 


262 


OPTICS. 


the   axis    CG   of  the   incident    rays,    is    united    on   a 
secondary  axis  parallel  with  CE,  at  the  point  where  this 


FIG.  146. 


Explanation  of  diffraction  taking  place  through  a  slit. 

strikes  the  focal  plane.  The  lens,  however,  as  has  been 
already  pointed  out  (§  102),  exercises  no  influence  on  the 
difference  of  path  of  the  rays  within  the  fasciculus.  These 
unite  in  the  focal  point  with  the  same  differences  of  path 
which  were  already  present  before  it  reached  the  lens. 

If  from  the  point  D  we  let  fall  the  perpendicular 
D  H  upon  CE,  C H  constitutes  the  extent  to  which  the 
path  of  the  marginal  ray  CE  exceeds  the  path  of  the  mar- 
ginal ray  DF  to  the  point  of  union.  And  for  each  of  the 
ther  innumerable  rays  of  the  diffracted  fasciculus  there 
is  a  portion  between  D  C  and  D  H,  to  which  extent  it 
falls  behind  the  ray  D  F. 

Those  elementary  rays  which  form  the  continuation 
of  the  incident  rays  do  not  indeed  in  any  way  differ 
from  one  another,  and  consequently  meet  in  the  chief 
focal  point  of  the  objective  in  the  centre  of  the  diffrac- 
tion image  in  perfect  unison.  The  larger,  however,  the 
diffraction  angle  becomes,  and  the  more  the  diffracted 
fasciculus  is  inflected  as  regards  the  axis  of  the  incident 


DIFFRACTION   OF  LIGHT.  263 

rajs,  the  larger  proportionately  becomes  the  difference 
of  path,  C  H,  of  its  marginal  rajs. 

With  a  certain  small  value  of  the  angle  $,  CH 
must  be  equal  to  half  a  wave-length  of  the  incident 
homogeneous  light.  The  marginal  raj  CE  will  then 
be  in  complete  discordance  with  the  marginal  raj 
D  F.  These  two  rajs  must  therefore  neutralise  each 
other  at  the  point  where  thej  meet.  The  innumerable 
other  rajs  of  the  fasciculus,  on  the  other  hand,  have 
but  little  difference  of  path;  they  are  not  therefore  in 
complete  discordance  with  each  other,  but  at  the  same 
time  thej  are  not  in  perfect  accordance.  A  certain 
amount  of  light  will  therefore  be  present  at  their  point 
of  union,  but  this  will  be  less  than  in  the  centre  of  the 
image. 

If  the  angle  of  diffraction  <j>  be  so  large  that  C  H 
is  equal  to  an  entire  wave- length,  the  middle  ray  (6) 
of  the  fasciculus  is  retarded  a  half  wave-length  as  com- 
pared with  the  ray  D  F,  and  is  neutralised  by  it  where 
they  meet.  The  same  thing  happens  with  the  pairs  of 
rajs  1  and  7,  2  and  8,  5  and  11,  which  differ  in  their 
paths  to  the  extent  of  a  half  wave-length.  Since,  conse- 
qiuntlj,  every  ray  of  the  fasciculus  finds  a  companion 
which  is  in  complete  discordance  with  it,  darkness 
must  prevail  at  the  point  where  they  meet.  At  this 
spot  therefore,  reckoning  from  the  middle  of  the  image, 
the  first  dark  stria  must  occur. 

If  now,  with  still  greater  inclination  of  the  diffracted 
rays,  the  difference  of  path  of  the  marginal  rajs  amounts 
to  three  half  wave-lengths,  it  maj  be  conceived  that 
the  beam  is  divided  bj  the  rajs  4  and  8  into  three 
equal  parts.  Thus  the  raj  8  is  a  whole  wave-length  be- 
hind the  raj  DF-,  the  part  of  the  fasciculus  contained 


264  OPTICS. 

between  them  undergoes,  as  has  already  been  shown, 
extinction,  only  the  last  third,  the  marginal  rays  oi 
which  differ  by  a  semi-undulation,  produces  the  effect  of 
light  at  the  point  of  union.  But  as  this  only  contains 
a  third  of  the  whole  amount  of  rays,  whilst  it  otherwise 
exhibits  the  same  difference  of  path  as  the  entire  fasci- 
culus previously  considered,  with  the  marginal  ray  dif- 
ference of  a  semi-undulation,  the  aether  particles  found 
at  the  point  of  union  can  only  possess  a  three  times 
smaller  amplitude  of  vibration  than  the  complete  fascicu- 
lus. And  since  the  intensity  of  light  (see  §  96)  is  always 
proportional  to  the  square  of  the  amplitude  of  vibration, 
it  is  obvious  that  the  illumination  at  the  point  of  union 
of  the  fasciculus  having  a  difference  of  three  half  wave- 
lengths in  the  marginal  rays,  is  only  the  ninth  part 
of  that  which  the  fasciculus  with  a  difference  of  path  of 
a  half  wave-length  produces. 

When  with  progressively  increasing  angle  of  diffrac- 
tion the  difference  C  H  of  the  marginal  rays  is  equal  to 
two  entire  wave-lengths,  the  middle  ray  ((>)  remains  a 
whole  wave-length  behind  C  F,  and  the  ray  D  E  a  whole 
wave-length  behind  the  middle  ray. 

Each  half  of  the  beam  now  has  in  itself  the  means 
of  its  extinction.  Similarly,  it  may  easily  be  com- 
prehended that  every  diffracted  fasciculus  of  rays,  the 
marginal  rays  of  which  differ  in  their  path  any  number 
of  whole  wave-lengths,  must  disappear.  The  dark  lines 
in  the  diffraction  image  of  the  slit  (fig.  142)  correspond 
to  these  differences  of  path.  The  middle  of  the  bright 
areas  between  each  pair  of  dark  strite  corresponds  to 
the  fasciculi  whose  marginal  ray  differences,  3,  5,  7 
.  .  .  amount  to  an  unequal  number  of  half  wave- 
lengths. The  intensity  of  light  at  these  spots  amounts 


DIFFRACTION   OF  LIGHT.  265 

to  -|,  -J3-,  -fg  ....  as  compared  with  that  which  exists 
at  those  points  where  the  difference  of  the  marginal 
rays  equals  one  half  wave-length ;  these  lie  in  the 
middle  brightest  area,  which  is  twice  the  width  of  each 
lateral  one. 

114.  In  the  right-angled  triangle  CDS' (fig.  146) 
the  angle  at  D  is   equal  to  the  diffraction  angle  <j> ;  if 
therefore  the  angle  </>  and  the  width  C  D  of  the  slit  be 
measured,  we  can  easily  estimate  the  length  C  H.     The 
telescope  of  a  Theodolite  serves  for  the  measurement  of 
the  angle  <£  (fig.  109).    If  it  be  first  arranged  in  such  a 
manner  that  its  crossed  threads  are  in  the  centre  of 
the  image,  and  it  be  rotated  laterally  till  the  first  dark 
line  appears  at  the  crossed  threads,  the  diffraction  angle 
can  be  read  off  on  the  horizontal  circle  of  the  instru- 
ment ;  the  corresponding  value  of  C  H  must  then  be 
equal  to  the  wave-lengths   of  the  homogeneous  light 
employed.     Schwerd,  for  example,  found  that  when  red 
glass  was  used  and  the  width  of  the  slit  was  1*353  mm., 
the  first  dark  line  corresponded  to  a  diffraction  angle  of 
V  38",  which  gave  for  that  particular  red  light  a  wave- 
length of  643  millionths  of  a  millimeter. 

Although  the  explanation  we  have  given  of  the  dif- 
fraction phenomena  produced  by  a  slit-shaped  aperture 
refers  only  to  the  appearances  presented  when  a  tele- 
scope is  employed,  it  will  still  hold  for  a  diffraction 
image  thrown  upon  a  screen,  if  this  be  removed  to  such 
a  distance  from  the  aperture  that  all  the  rays  passing 
to  any  point  of  the  screen  may  be  regarded  as  parallel 
to  each  other. 

115.  An  inexhaustible  variety  of  the  most  beautiful 
phenomena  of  diffraction  may  be  produced  by  making 
a  group   of  several  or  numerous  apertures  instead  of  a 


266  OPTICS. 

single  one.  If,  for  example,  a  number  of  fine  wires  be 
stretched  in  a  frame,  the  interspaces  between  them  form 
so  many  slits,  and  we  have  a  kind  of  grating.  Such  a 
grating  of  extraordinary  delicacy  may  be  obtained  by 
cutting  parallel  lines  at  equal  distances  from  each  other  on 
glass  with  a  diamond.  The  lines  drawn  with  the  diamond 
correspond  to  the  wires,  and  the  unscratched  surface  of 
the  glass  to  the  interspaces  of  the  wires. 

If  a  fasciculus  of  solar  rays  be  allowed  to  pass 
through  the  slit  of  a  Heliostat  and  to  fall  upon  a 
lens  which  projects  a  sharp  image  of  the  slit  upon 
the  adjacent  screen,  and  if  a  fine  glass  grating  be 
placed  in  front  of  the  lens,  a  beautiful  figure  will  be- 
come visible  upon  the  screen  (fig.  147).  Symmetri- 

FlG.  147. 


Diffraction  phenomena  through  a  grating. 

cally  to  the  two  sides  of  the  white  image  of  the  slit 
a  series  of  spectra  appear,  the  violet  end  of  which  is 
turned  inwards  whilst  the  red  is  external.  Whilst  the 
two  spectra  on  either  side  of  the  centre  are  isolated,  the 
succeeding  ones,  which  are  progressively  both  broader 
and  fainter,  partially  overlap  each  other.  In  these 
spectra,  especially  in  the  first  and  second  on  either 
side,  the  well-known  lines  of  Fraunhofer  are  distinctly 
visible. 

The  same  appearances  are  presented  if  the  grating 
be    held    in   front   of    the    objective    of    a    telescope 


DIFFRACTION   OF  LIGHT. 


267 


Fia.  148. 


placed  at  a  little  distance  from  the  slit.  On  the  sup- 
position that  this  method  of  observation  is  adopted, 
an  attempt  may  be  made  to  explain  the  origin  of  these 
spectra. 

In  fig.  148  let  A  B  represent  the  transverse  section 
of  the  grating,  and  M  a  N  the  direction  of  the  inci- 
dent rays  falling  vertically 
to  the  plane  of  the  grating. 
All  fasciculi  of  rays  running 
parallel  to  each  other,  i.e., 
with  the  same  diffraction 
angle  <£  at  the  bright  inter- 
spaces of  the  grating,  are 
united  by  the  objective  lens 
at  the  same  spot  of  the 

image-plane.      Disregarding    Explanation  of  diffraction  through  a 
for  the  moment  the  difference 

of  path  which  exists  amongst  the  elementary  rays 
of  each  fasciculus,  let  us  turn  our  attention  to  the 
difference  of  path  of  the  several  fasciculi  in  regard 
to  each  other.  If  from  the  point  c,  from  which  the 
first  ray  of  the  second  fasciculus  proceeds,  a  perpen- 
dicular, c  h,  be  let  fall  upon  the  first  ray  of  the  first 
fasciculus,  a  h  obviously  represents  the  extent  to  which 
the  first  fasciculus  is  retarded  as  compared  with  the 
second,  and  consequently  as  each  fasciculus  is  retarded 
as  compared  with  the  next  succeeding  one.  If  we 
now  suppose  the  light  to  be  homogeneous,  as  for 
example  Sodium  light,  and  the  line  a  h  equal  to  its 
wave-length,  the  whole  of  the  fasciculi  will  be  in  com- 
plete accordance,  and  co-operate  with  one  another  at 
the  point  of  union  to  give  greater  intensity  of  light. 
If  the  observer  move  to  a  very  slight  extent  from  that 


268  OPTICS. 

position  in  which  the  difference  of  path  of  two  adjoin- 
ing fasciculi  amounts  to  a  whole  wave-length,  the  fasci- 
culi of  rays  must  mutually  extinguish  each  other  at  the 
point  where  they  meet.  If,  for  example,  with  a  grating 
of  1 ,000  lines  the  angle  of  diffraction  increases  to  such 
an  extent  only  that  the  first  fasciculus  is  retarded  as 
compared  with  the  second  1  +  -y-oVo  wave-lengths,  it 
is  retarded  as  compared  with  the  third  2  -f  1  0*0  0  ;  as 
compared  with  the  fourth  3  -f-  y^Vo"?  an(^  so  on  until  as 
compared  with  the  501st  it  is  retarded  to  the  extent 
of  500  -f  Jyyk,  or  500  +  i  of  a  wave-length.  The 
501st  fasciculus  is  thus  in  complete  discordance  with 
the  first,  and  similarly  the  502nd  with  the  second,  the 
503rd  with  the  third,  and  so  on,  until  lastly  the  500 tli 
with  the  1000th.  If,  with  a  somewhat  greater  angle  of 
diffraction,  the  difference  of  path  between  the  first  and 
second  fasciculus  were  1  4-  yj-g-  wave-length,  the  51st 
fasciculus  would  be  in  complete  discordance  with  the 
first,  and  the  fasciculi  must  again  extinguish  each  other 
in  pairs  where  they  meet.  Speaking  generally,  as  soon 
as  they  recede  on  either  side  from  the  above  direc- 
tion, in  which  ah  is  equal  to  a  whole  wave-length, 
neutralisation  of  the  waves  occurs,  providing  only  that 
the  increase  or  decrease  of  a  h  is  less  than  an  entire 
wave-length. 

For  if  ah  be  equal  to  two  entire  wave-lengths,  all 
the  fasciculi  are  again  in  complete  accordance,  and  so 
on  each  occasion  the  difference  of  path  of  two  adjoining 
fasciculi  is  equal  to  any  number  of  entire  wave-lengths. 

The  diffraction  image  perceived  when  Sodium  light 
is  used  is  consequently  very  simple.  In  the  middle  of 
the  field  of  vision  is  the  image  of  the  slit ;  then  follows 
at  a  certain  distance  on  each  side,  which  corresponds  to 


DIFFRACTION   OF  LIGHT.  269 

the  difference  of  path  of  a  whole  wave-length,  a  slender 
yellow  line  upon  a  perfectly  black  ground;  then  at 
double  the  distance,  corresponding  to  the  difference  of 
path  of  two  wave-lengths,  is  a  second  bright  line,  and 
others  still  at  thrice,  fourfold,  &c.  distances.  One  or 
the  other  of  these  pairs  of  lines  can  only  then  vanish 
when  each  of  the  fasciculi  by  which  they  are  pro- 
duced already  carries  in  it  the  germ  of  neutralisa- 
tion, that  is,  when  the  lines  fall  directly  011  the  spots  at 
which  each  interlinear  space  of  the  grating  would 
exhibit  a  dark  stria.  Moreover,  the  diminution  in 
the  intensity  of  the  light,  which  in  general  occurs  in 
the  consecutive  lines,  is  to  be  ascribed  to  the  inter- 
ference which  takes  place  in  the  interior  of  each  separate 
fasciculus. 

For  every  other  homogeneous  kind  of  light  a  series 
of  bright  lines  of  that  particular  light  would  be  perceived, 
which,  however,  lie  nearer  the  image  of  the  slit  when 
the  wave-lengths  are  smaller,  and  on  the  other  hand, 
more  remote  when  the  wave-lengths  are  greater.  When 
white  light  is  employed  the  strise  which  correspond  to 
the  difference  of  path  of  each  of  the  wave-lengths  occur 
according  to  the  serial  succession  of  their  wave-lengths, 
and  form  the  first  grating  spectrum  on  each  side  of  the 
white  image  of  the  slit ;  the  second,  third,  and  following 
spectra  in  the  same  way  correspond  to  the  greater  diffe- 
rences of  path.  When  certain  kinds  of  rays  are  absent 
in  the  incident  light  it  is  obvious  that  hiatuses  must 
exist  at  the  corresponding  points  in  the  spectra,  as  for 
example  at  the  Fraunhofer's  lines  when  sunlight  is 
used. 

116.  Owing  to  the  occurrence  of  Fraunhofer's  lines 
in  the  grating  spectrum,  we  are  in  a  position  to  deter- 


270  OPTICS. 

mine   accurately   the    wave-lengths    corresponding;    to 
them.     Fraunhofer  himself,  to  whom  we  are  indebted 
for  the  discovery  of  the  grating  spectrum,  measured 
with  the  aid  of  the  Theodolite  the  wave-lengths  of  the 
lines  named  after  him  with  great  precision.     The  spec- 
trometer  (fig.    110)    is    still   better    adapted   for   these 
measurements.     If  we  place,  for  example,  the  grating 
instead  of  the  prism  upon  the  table  of  the  spectrometer, 
and  gradually  focus  the   telescope  upon  the   lines  of 
Fraunhofer,  the  angle  of  diffraction  corresponding  to 
each  focussing  can  be  read  off  upon  the  divided  circle. 
From  the  right-angled  triangle  a  ch  (fig.  148),  in  which 
the  angle  at  c  is  equal  to  the  measured  angle  of  diffrac- 
tion, and  the  side  a  c  is  likewise  known  as  the  sum  of  the 
breadth  of  a  grating  line  and  of  an  intervening  space, 
the  length  a  h  is  obtained,  which  is  equal  to  a  wave- 
length, or  is  equal  to  two,  three,  and  so  forth  wave- 
lengths, according  as  the  measurement  is  taken  in  the 
first,  or  second,  third,  and  so  on,  grating  spectrum.     The 
measurement  of  the  spectra  of  the  higher  serial  num- 
bers serves  to  control  the  values  furnished  by  the  first 
spectrum.     By  means  of  this  method  "Angstrom  has 
discovered   the  wave-lengths  which  are   given   in  the 
following  table  in  millionth s  of  a  millimeter  :  — 


A    760,4 
D,  589,5 
F    486,0 

B    686,7 
D2  588,9 
G    430,7 
H2  393,3. 

C    656,2 
E    526,9 
H,  396,8 

117.  By  means  of  the  grating  we  have  acquired  a 
knowledge  of  the  mode  in  which  compound  light  may 
be  broken  up  into  its  homogeneous  components  without 
any  assistance  from  the  refraction  and  dispersion  of 


DIFFRACTION   OF  LIGHT.  271 

colour  produced  by  a  prism.  The  grating  spectrum  is 
therefore  free  from  the  influences  which  the  nature  of 
the  material  of  which  the  prism  is  composed  exercises 
upon  the  arrangement  of  the  colours  in  the  prismatic 
spectrum.  In  a  grating  spectrum  the  several  homo- 
geneous rays  are  arranged  essentially  according  to  the 
differences  of  their  wave-lengths  in  air,  and  therefore 
according  to  a  property  which  is  inherent  in  the  rays 
themselves.*" 

The  grating  spectrum  is  therefore  to  be  regarded 
as  the  normal  spectrum  in  which  the  position  assign- 
able to  each  homogeneous  ray  in  consequence  of  its 
wave-length  is  not  in  any  way  altered  by  foreign  in- 
fluences. 

FIG.  149. 


Comparison  of  the  prismatic  with  the  grating  spectrum. 

A  comparison  of  the  prismatic  spectrum  with  a 
grating  spectrum  of  equal  length  (fig.  149)  enables  the 
influence  which  the  colour-dispersing  material  exercises 
upon  the  arrangement  of  the  colours  to  be  recognised. 

*  The  number  of  undulations  is  always  to  be  regarded  as  the  distin- 
guishing characteristic  of  a  homogeneous  colour.  In  the  propagation  of 
light  in  free  (ether  and  in  the  air,  which  occurs  with  equal  rapidity  for  all 
kinds  of  rays,  the  number  of  undulations  is  always  inversely  proportional 
to  the  wave-lengths,  and  these  may  therefore  be  regarded  as  characteristic 
as  those  of  the  pitch  of  tone. 
19 


272  OPTICS. 

The  middle  of  the  grating  spectrum  is  obviously  occu- 
pied by  those  colours,  the  wave-lengths  of  which  aie 
intermediate  between  those  of  the  extreme  visible  rays 
A  and  Hy  The  wave-length  576,8,  which  is  exactly 
intermediate  between  the  greatest,  760,4,  and  the 
smallest,  393,3,  corresponds  to  the  yellow  behind 
D.  This  colour  therefore  appears  in  the  middle  of 
the  grating  spectrum,  whilst  in  the  prismatic  spec- 
trum it  is  displaced  towards  the  red  end.  Owing  to 
prismatic  dispersion  the  deeper  tints  of  colour  are 
approximated  to  each  other,  whilst  the  lighter  tints  on 
the  contrary  are  more  widely  separated  than  in  the 
colour  scale  of  the  grating  spectrum  at  the  same  time 
rising  progressively  with  the  wave-lengths. 


CHAPTER  XX. 

COLOURS  OF  THIN  PLATES. 

118.  THE  lovely  play  of  colours  on  the  soap  bubble, 
well  known  to  all  from  the  happy  days  of  childhood, 
long  ago  excited  the  attention  of  the  physicist.  Hooke 
more  than  200  years  ago  was  aware  of  the  fact  that 
every  transparent  body,  if  sufficiently  thin,  exhibited 
similar  colours.  He  observed  further  that  the  fleetinu- 

O 

colours  of  the  soap  bubble  were  arranged  circularly 
around  the  thinnest  spot  of  the  fluid  membrane,  and  he 
was  soon  successful  in  producing  a  permanent  series  of 
rings  of  colour  by  placing  a  very  slightly  curved  piano- 


Newton's  colour-glass. 

convex  lens  with  its  curved  surface  upon  a  plane  glass 
plate  (fig.  150).  This  simple  apparatus,  however,  as  well 
as  the  rings  exhibited  in  it,  are  indissolubly  associated 
with  the  celebrated  name  of  Newton,  because  he  mea-l 
sured  the  phenomenon  and  established  the  laws  of  the! 
appearances  presented. 

If  a  large  specimen  of  a  Newton's  colour- glass, 
showing  the  colours  well,  be  taken,  and  a  broad  parallel 
beam  of  white  light  be  allowed  to  fall  upon  it,  whilst  a 
lens  is  placed  in  the  path  of  the  reflected  rays,  a  beauti- 
fully coloured  system  of  alternately  bright  and  dark 


274  OPTICS. 

rings  (fig.  151)  will  be  seen  upon  the  screen  behind  the 
lens,  which  are  more  and  more  closely  approximated 
FIG.  isi.  fr°m  within  outwards,  and  gra- 

dually become  indistinct.  The 
common  centre  of  all  the  rings, 
is  black.  The  colours  from  the 
centre  to  the  first  dark  ring  were 
named  by  Newton  colours  of  the 
first  order ;  from  this  to  the  se- 
cond dark  ring  follow  the  colours 
of  the  second  order,  and  so  on. 

Newton's  coloured  rings.  r,,,  , 

These  colours  are — 

First  Order  :  black,  pale  blue,  white,  orange,  yellow, 
red. 

Second  Order  :  violet,  purple,  yellowish-  green,  yel- 
lowish-red. 

Third  Order :  purple,  indigo,  green,  yellow,  rose, 
carmine. 

Fourth  Order  :  bluish-green,  yellowish-red,  pale  red. 

Fifth  Order :  pale  green,  white,  pale  red. 

If  the  lens  be  placed  behind  the  colour-glass  so  that 
it  now  receives  the  transmitted  rays,  a  system  of  rings 
is  still  seen  upon  the  screen,  the  colours  of  which  how- 
ever are  much  fainter  than  they  were  previously  in  the 
reflected  light.  The  centre  of  these  rings  is  white,  and 
their  colours  are  arranged  in  complementary  succession 
to  those  of  the  reflected  rays.  When  homogeneous  light 
is  employed — if  for  example  the  incident  rays  be  allowed 
to  pass  through  a  red  glass — the  rings  appear  in  both 
cases  merely  alternately  bright  and  dark ;  and  in  the 
transmitted  light  it  may  be  observed  that  the  dark 
rings  occupy  exactly  the  position  of  the  bright  rings  in 
the  reflected  light. 


COLOUES  OF  THIN  PLATES.  275 

119.    An  attempt  will  now  be  made  to  explain  the 
mode  of  origin  of  these  phenomena.     In  fig.  152,  let 
MNPR  represent  a  thin  layer  of  a  trans-          FIG.  152. 
parent  substance — for  example,  a  piece 
of  thin    glass — upon    which   a   beam  of 
parallel   rays  falls   in   the  direction  a  b.    M__^//c      N 
Every  ray,  a  b,  is  in  part  reflected  at  the 
anterior  surface,  towards  o,  whilst  it  is  in 
part  refracted  towards  d ;  at  d,  before  it 
leaves  the  lamina  in  the  direction  d  h,  it    ExCoioursIOIJ>f°£  the 
undergoes  a  second  reflexion ;  and  at  the 
posterior  surface,  P  R,  a  portion  of  the  light  here  reflected 
reappears  parallel  with  b  o  at  the  anterior  surface. 

Disregarding  the  transmitted  portion  of  each  ray, 
d  h,  let  us  in  the  first  place  consider  the  rays  which 
leave  the  plate  parallel  with  b  o  after  being  reflected  in 
part  at  the  anterior  surface  H  N,  and  in  part  at  the 
posterior  surface  PR. 

For  each  incident  ray,  a  6,  which  is  reflected  at  the 
anterior  surface  towards  o,  there  is  an  adjacent  ray, 
/c,  the  portion  of  which  reflected  from  the  posterior 
surface  at  n,  on  emerging  from  the  anterior  surface, 
follows  the  same  path,  b  o.  Of  the  two  rays  which 
pursue  the  same  path,  b  o,  the  second,  because  it  has 
had  to  traverse  the  path  c  n  b  within  the  film,  is  re- 
tarded, as  compared  with  the  other ;  to  this  retardation, 
which  is  obviously  greater  in  proportion  as  the  film  is 
thicker,  there  is  still  a  further  retardation,  dependent 
on  the  circumstance  that  the  one  ray  is  reflected  in  the 
denser,  the  other  in  the  rarer  medium ;  the  reflexion  in 
the  denser  medium,  as  has  already  been  shown  (§  101), 
leading  to  a  retardation  of  a  half  wave-length. 

If,    for   example,    the    retardation   within    the  film 


27(5  OPTICS. 

amounts  to  a  half  wave-length  of  the  red  light,  the  two 
rays  coursing  along  the  line  b  o  are  in  complete  accord- 
ance, because  in  being  reflected  the  one  is  retarded  a  half 
wave-length ;  the  film  therefore,  if  it  be  illuminated  with 
red  light,  appears  to  an  observer  at  o  bright.  The  same 
would  occur  when  the  films  are  of  three  or  five  times 
greater  thickness,  because  in  these  a  retardation  amount- 
ing to  3,  5,  and  so  on,  half  wave-lengths  occur.  On  the 
other  hand,  films  which,  on  account  of  their  thickness, 
bring  about  retardations  equal  to  a  number  of  whole 
wave-lengths,  and  which  are  consequently  2,  4,  6  .... 
times  as  thick  as  the  first-considered  film,  appear  dark 
with  red  light,  because  the  two  rays  coursing  towards  60, 
since  they  differ  in  their  path  by  an  unequal  number  of 
half  wave-lengths,  are  in  discordance.  Were  the  in- 
cident light  white,  a  film  which  retards  red  light  a 
whole  wave-length  would  extinguish  the  red,  but  not  the 
other  colours,  the  wave-lengths  of  which  are  different. 
The  film  would  consequently  exhibit  a  greenish  tint, 
resulting  from  the  mixture  of  all  colours  not  ex- 
tinguished ;  and  were  another  film  sufficiently  thin  to 
extinguish  the  yellow  rays,  it  would  appear  blue  with 
white  light,  and  so  on. 

120.  A  film  of  perfectly  equal  thickness  throughout 
will  consequently  exhibit  the  same  colour  in  its  whole 
extent — that,  namely,  which  corresponds  to  its  thick- 
ness. 

In  Newton's  colour-glass  we  have  to  do  with  the 
film  of  air  intervening  between  the  two  glasses,  tin* 
thickness  of  which,  proceeding  from  the  point  where 
the  convex  lens  and  the  glass  plate  are  in  contact,  in- 
creases in  all  directions  from  the  centre  outwards.  At 
[  the  point  of  contact  itself,  where  the  thickness  of  the 


COLO  UBS   OF  THIN  PLATES.  277 

film  and  consequently  also  the  difference  of  path  depend-  ^ 
ing  upon  it,  is  nil,  there  is  only  a  difference  of  path  of  a  S 
half  wave-length,  caused  by  the  dissimilar  reflexion  of  | 
the  two  rays ;  there,  consequently,  is  an  extinction  ol 
light,  and  we  see  at  this  point  a  dark  spot.  If  we  pass 
outwards  from  the  point  of  contact  we  meet  with  suc- 
cessive spots  where  the  total  difference  of  path  for 
every  homogeneous  colour  amounts  to  2,  3,  4,  5  .... 
half  wave-lengths,  and  where,  consequently,  alternate 
increase  and  extinction  of  light  must  occur.  Thus  we 
obtain  an  explanation  of  the  system  of  rings  with  dark 
central  point,  even  with  homogeneous  light.  The  smaller 
the  wave-length  the  narrower  must  the  rings  be.  When 
white  light  is  used,  neither  the  bright  nor  the  dark 
rings  of  the  different  colours  can  therefore  coincide,  but 
in  every  concentric  circle  proceeding  outwards  from  the 
centre,  the  colour  resulting  from  the  mixture  of  all  the 
colours  which  have  escaped  extinction  must  make  its 
appearance. 

Let  us  now  return  to  the  thin  lamina  MNPR 
(fig.  152),  and  consider  the  ray  dh  which  leaves  the 
film  after  it  has  traversed  it  along  the  line  b  d.  With 
it  is  also  associated  a  second  ray,  which  after  it  has 
been  reflected  along  the  path  fcnbd,  and  at  n  and  b 
has  been  reflected  inwards,  has  undergone  a  retardation 
compared  with  the  others  which  corresponds  to  the 
length  cnb.  Since  two  reflexions  take  place  either  in 
the  denser  or  the  rarer  medium,  they  either  cause 
no  difference  of  path  or  produce  together  a  difference 
of  a  whole  wave-length,  and  alter  therefore  in  no 
degree  the  amount  of  coincidence  or  of  opposition 
of  the  two  rays  which  the  film  occasions  in  consequence 
of  its  thickness.  The  transmitted  rays  are  conse- 


278  OPTICS. 

quently  in  complete  accordance  when  the  reflected  rays 
are  in  discordance,  and  vice  versa.  We  see  therefore 
in  Newton's  colour-glass,  with  transmitted  homoge- 
neous light,  a  bright  centre  and  bright  rings  at  those 
points  where  with  reflected  light  the  centre  and  the 
rings  are  dai'k ;  and  in  the  same  way  with  white  light 
illumination  the  mixed  colours  are  in  the  latter  case 
complementary  to  those  in  the  former. 

But  why  is  it  that  the  rings  appear  so  very  much 
paler  by  transmitted  as  compared  with  reflected  light  ? 
The  answer  is  easily  given  ;  of  the  two  rays  which  run 
in  the  direction  d  K,  one,  on  account  of  its  ha,ving  under- 
gone two  reflexions,  is  much  fainter  than  the  other.  The 
two  rays  therefore,  even  when  they  are  in  complete 
discord,  can  never  entirely  extinguish  one  another.  On 
the  other  hand,  the  two  rays  reflected  towards  b  o,  of 
which  each  has  been  once  reflected,  are  of  nearly  equal 
strength,  and  must  consequently,  as  often  as  their  dif- 
ference of  path  amounts  to  an  odd  multiple  of  a  half 
wave-length,  undergo  complete  extinction.  It  is  plain 
that  the  liveliness  of  the  colours  depends  on  the  com- 
pleteness of  the  interference. 

121.  But  even  in  the  reflected  rings,  as  we  proceed 
from,  within  outwards,  and  as  the  film  of  air  becomes 
progressively  thicker,  it  may  be  observed  that  there  is 
a  decided  diminution  in  the  brilliancy  of  the  colours, 
until  the  most  external  pale  rings  gradually  disappear 
in  a  uniform  white.  It  is  easy  again  to  explain  why  a 
thicker  film  exhibits  no  colours,  appearing  when  illumi- 
nated by  white  light  simply  white.  Let  it  be  granted, 
for  example,  that  a  film  is  just  so  thick  that  it  retards 
the  red  rays  (B)  about  ten  wave-lengths,  apart  from 
the  retardation  of  a  half  wave-length  which  depends 


COLOURS  OF  THIN   PLATES.  279 

on  the  dissimilar  reflexions.  Now  since  in  the  same 
length  which  includes  10  red  waves  there  are  about 
1 7  wave-lengths  of  violet,  the  same  film  causes  a  diffe- 
rence of  path  in  the  violet  rays  amounting  to  17  wave- 
lengths. Between  the  former  red  and  these  violet 
rays  there  are  still  other  rays  with  11,  12,  13,  14,  15, 
16  wave-lengths  in  the  same  space  which  contains  10 
waves  of  the  B-red.  The  colours  which  correspond  to 
these  rays  are  in  succession  orange,  greenish-yellow, 
green,  bluish-green,  bright-blue,  indigo.  All  these 
rays  must  disappear  in  reflected  light  because  the  film 
causes  in  them  a  difference  of  path  of  an  odd  number  of 
half  wave-lengths.  Those  rays,  however,  the  wave- 
lengths of  which  are  contained  10J,  11^,  12J,  13J,  14£, 
15^,  and  16  J  times  in  the  given  length,  because  they 
strengthen  each  other,  are  seen  of  great  brightness  in 
reflected  light.  But  to  these  the  following  colours  cor- 
respond in  succession:  bright-red,  yellow,  yellowish- 
green,  dark-green,  blue,  indigo- violet.  An  observer 
looking  at  the  plate  must  obviously  receive  from  the 
mixture  of  these  colours  the  impression  of  white  light. 

122.  That  the  colours  first  named  are  really  absent 
in  reflected  light  may  be  easily  demonstrated  by  the 
following  experiment.  The  solar  rays  are  to  be  allowed 
to  fall  upon  a  plate  of  Mica,  which  to  the  naked 
eye  appears  white.  The  reflected  rays  are  then  made 
to  traverse  a  slit,  and  are  dispersed  into  a  spectrum  by 
means  of  a  prism  in  the  usual  way.  In  this  spectrum, 
between  the  red  and  the  violet,  eight  dark  stride  (fig.  153) 
are  perceptible,  corresponding  to  those  kinds  of  rays 
which  are  extinguished  by  interference.  A  thicker 
plate  of  Mica  is  now  to  be  selected,  and  the  spectrum 


280  OPTICS. 

now  presents  a  very  great  number  01  dark  interference 
lines  (Miiller's  lines). 


FIG. 153. 


A  EC'  I)       E 

II II  Illl 


Interference  stride  in  the  spectrum. 

The  spectrum  of  the  light  reflected  from  the  Mica 
plate  may  be  received  upon  a  paper  screen  painted  over 
with  solution  of  quinine,  and  thus  rendered  fluorescent; 
and  it  will  then  be  observed  that  in  the  now  visible 
ultra-violet  part  of  the  spectrum  such  dark  interference 
striae,  make  their  appearance.  And  just  as  from  the 
relation  of  the  wave-lengths  of  red  and  violet  the 
number  of  lines  within  the  visible  spectrum  was  for- 
merly determined,  we  are  now  able,  conversely,  from 
the  number  of  the  lines  that  we  can  count  from  the 
violet  to  the  end  of  the  ultra-violet,  to  determine  the 
ratio  of  the  wave-lengths  of  the  extreme  ultra-violet 
rays  to  those  of  the  violet  rays,  and  consequently  as 
the  wave-lengths  of  all  visible  rays  are  known,  to  deter- 
mine the  wave-lengths  of  the  most  refrangible  ultra- 
violet rays. 

By  an  experiment  essentially  similar  to  the  above, 
Esselbach  found  that  the  wave-lengths  of  the  line  R 
amount  to  309  millionths  of  a  millimeter. 

Becquerel  received  the  spectrum  of  solar  light  re- 
flected from  a  film  of  Mica  on  a  screen  covered  with 
a  phosphorescent  substance,  and  was  able  to  follow  the 
interference  lines  into  the  ultra-red  region,  where  the 


COLOURS  OF  THIN  PLATES.  181 

rays  act  in  the  peculiar  manner  mentioned  above  (§81), 
namely,  apparently  conversely  to  the  more  refrangible 
part  of  the  spectrum.  From  the  measurements  ob- 
tained it  resulted  that  the  wave-lengths  of  the  ex- 
treme ultra-red  rays  in  this  way  rendered  visible  are 
more  than  twice  the  length  of  the  extreme  red  rays. 
According  to  another  less  direct  method,  Miiller  deter- 
mined the  wave-lengths  of  the  extreme  ultra-red  at 
about  4,800  raillionths  of  a  millimeter. 

In  music  one  note  is  said  to  be  an  octave  above 
another  if  the  number  of  its  undulations  is  double,  and 
consequently  its  wave-lengths  half  as  great  as  the 
latter.  If  the  same  nomenclature  be  employed  in  the 
matter  of  colours,  it  may  be  said  that  the  visible 
spectrum  from  A  to  H  does  not  occupy  a  complete 
octave,  but  reaches  from  the  fundamental  note  C  to  the 
sharp  sixth  a  is.  If,  however,  the  solar  spectrum  be 
considered  in  its  whole  extent,  we  find  in  the  ultra-red 
alone,  according  to  Miiller,  more  than  two  octaves,  to 
which  must  be  added  more  than  another  octave  from  A 
to  the  line  R  in  the  ultra-violet.  The  whole  length  of 
the  solar  spectrum,  thus  embraces  consequently  about  four 
octaves. 


282  OPTTCa 


CHAPTER  XXI. 

DOUBLE    REFKACTION. 

123.  WHEN  after  almost  two  thousand  years  of  vain 
attempts  on  the  part  of  the  most  accomplished  mathe- 
maticians from  Ptolemy  to  Kepler,  to  discover  the  law 
of  refraction,  i.e.  the  geometric  relation  between  the 
incident  and  the  refracted  ray  (see  §  30),  it  was  at  last 
discovered  in  the  year  1£20  by  Snellius,  the  ingenuity 
of  observers  was  taxed  afresh  in  1669  by  the  '  wonderful 
and  extraordinary  refraction  /,£  light'  discovered  by 
Erasmus  Bartholinus,  Professor  of  Geometry  in  Copen- 
hagen, in  the  beautiful  crystal  spar  from  Iceland. 

The  completely  colourless  and  transparent  calca- 
reous spar  depicted  in  the  adjoining  figure  is  bounded 
by  six  natural  plane  crystalline  surfaces,  of  which 
the  opposite  pairs  are  parallel  to  each  other.  If  a 
beam  of  parallel  rays  fall  perpendicularly  upon  one  of 
its  surfaces,  two  such  beams  are  seen  emerging  from 
the  opposite  one,  which  form  upon  a  screen  so  placed 
as  to  intercept  their  passage  two  equally  bright  white 
spots. 

This  phenomenon  is  termed  double  refraction,  and 
since  in  general  every  ray  of  light  traversing  the  spar 
is  split  into  two  rays,  all  objects  seen  through  such  a 
crystal  are  doubled. 


DOUBLE  REFRACTION.  283 

One  of  these  two  fasciculi,  as  it  emerges,   follows 
precisely  the  same  course  as  the  incident  one  would, 
if  it   traversed   an   ordinary  plate   of 
glass.     The  other,  on  the  contrary,  is 
laterally  displaced  in  a  direction  which 
is   dependent  on   the  position   of  the     r™      t~^^\ 
crystal.      If    the    crystal    be   rotated       iR  jj| 

without  altering  its  position  in  regard        ^ 
to  the  incident  light,  the  bright  spot 
which  belongs  to  the  first  beam  remains 
in  its  place,  whilst  the  spot  formed  by      Double  refraction  in 
the  second  beam,  following  the  move- 
ment of  rotation,  describes  a  circle  around  the  other. 

Again,  if  the  crystal  be  gradually  inclined  more  and 
more  to  the  incident  rays,  the  first  beam  exhibits  no- 
thing extraordinary  in  its  behaviour,  but  constantly 
pursues  the  direction  it  ought  to  have  in  accordance 
with  Snellius'  law  of  refraction.  These  rays  are  con- 
sequently termed  the  ordinarily  refracted  ones.  The 
other  beam  does  not  obey  this  law ;  it  neither  remains 
constant  in  the  plane  of  incidence,  nor  is  there  an  inal- 
terable ratio  between  the  angle  of  incidence  and  the 
angle  of  fraction  ;  this  ray  is  consequently  said  to  be 
extraordinarily  refracted. 

124.  The  index  of  refraction  of  the  ordinary  rays 
may  be  determined  in  the  usual  way  by  means  of  a 
prism  cut  from  the  crystal.  It  is  then  found  that  its 
ratio  of  refraction  (for  Sodium  light)  is  1*6585.  This 
number  indicates  that  the  velocity  of  propagation 
of  light  in  air,  as  compared  with  the  velocity  of  tho 
ordinary  ray  in  the  crystal,  is  as  1/6585  to  1,  or  that  if 
the  former  be  equal  to  unity,  the  latter  is  0*603. 

The  law  of  refraction  of  the  extraordinary  ray  is 


284 


OPTICS. 


F;G. 155. 


Rhombohedron. 


somewhat  complicated.  From  the  experiment  above 
made,  the  conclusion  may  in  the  first  place  be  drawn 
that  the  path  of  these  rays  stands  in  a  certain  relation 
to  the  form  of  the  crystal.  In  order  to  investigate  this 
law  we  must  therefore  first  consider  with  some  atten- 
tion the  crystalline  form  of  calcareous  spar.  Fig.  155 

represents  the  transparent 
model  of  a  cube  formed  of 
twelve  rods  of  equal  length 
which  are  united  at  their 
extremities  by  hinges.  If 
the  cube  be  placed  upon  one 
of  its  angles,  a,  and  the 
opposite  angle,  &,  be  pressed 
with  the  finger,  the  whole 
form  of  the  model  undergoes 
a  change,  the  two  compressed  angles,  a  and  fe,  become 
more  obtuse,  but  the  other  six  angles  more  acute  than 
before,  and  the  six  originally  square  surfaces  change 
into  diamonds  or  rhombs ;  the  cube  thus  altered  is 
called  a  rhombohedron.  Such  a  rhombohedron  is  the 
primary  form  of  Iceland  spar  (fig.  156,  a).  The 
straight  line,  a  b  (fig.  155),  connecting  the  two  obtuse 
angles,  is  characterised  by  the  circumstance  that  the 
surfaces,  edges,  and  angles  are  arranged  symmetrically 
around  it.  It  is  therefore  called  the  axis  of  the 
crystal. 

The  surfaces  and  borders  are  inclined  equally  to  the 
axis,  and  the  points  of  the  angles  and  borders  leading  to 
them  are  equally  distant  from  it. 

Crystals  of  Iceland  spar  are  not  unfrequently  found 
in  which  the  six  equal  acute  angles  are  replaced  by  six 
planes  paralled  to  the  axis  of  the  crystal.  The  six-sided 


DOUBLE   REFEACTION. 


285 


columnar   prisms   with  rhomboliedric  ends,   shown   in 
fig.  156,  b,  originate  in  this  way. 


FIG. 156. 


Crystalline  forms  of  Iceland  spar. 

In  other  instances  the  obtuse  angles  have  disap- 
peared, and  are  replaced  by  surfaces  which  are  perpendi- 
cular to  the  axis.  We  have  then  a  six-sided  columnar 
crystal  with  straight  terminal  planes  (fig.  156,  c).  By 
cutting  down  the  right  and  left  edges,  whilst  leaving 
the  anterior  and  posterior  edges  of  the  column  as  well 
as  the  two  terminal  surfaces,  a  rectangular  parallelepiped 
is  obtained,  the  upper  and  lower  surfaces  of  which  are  at 
right  angles  to  the  crystalline  axis,  whilst  the  remaining 
four  surfaces  are  parallel  to  it. 

125.  If  now  a  thin  beam  of  light  be  allowed  to 
fall  vertically  upon  the  anterior  and  posterior  surfaces 
of  such  a  crystal,  the  axis  of  which  is  vertical,  it  will 
be  seen  that  a  single  ray  emerges  from  the  opposite 
parallel  surface  in  direct  continuation  of  the  incident 
beam.  As  soon,  however,  as  the  crystal  is  turned  upon 
its  axis,  so  that  the  beam  strikes  more  and  more  ob- 
liquely upon  its  anterior  surface,  the  double  refraction 
becomes  more  and  more  obvious;  and  it  may  at  the 
same  time  be  remarked  in  regard  to  the  bright  spots 
upon  the  screen,  that  the  two  rays  into  which  the 
beam  is  divided  remain  constantly  in  a  plane  perpendi- 
cular to  the  axis.  Exact  investigation  shows  further 


286  OPTICS. 

that  in  this  case,  i.e.,  when  the  plane  of  incidence  is  at 
right  angles  to  the  axis  of  the  crystal,  both  rays  follow 
Snellius9  law  of  refraction.  If  therefore  a  prism  be  cut 
from  a  piece  of  Iceland  spar  in  the  manner  indicated  in 
fig.  156,  d,  the  refracting  edge  of  which,  ef,  is  parallel 
with  the  axis  of  the  crystal,  the  ratios  of  refraction  of 
both  rays  may  be  determined  by  means  of  it  in  the 
usual  manner.  For  the  more  strongly  deflected  ray  we 
find,  as  before,  the  number  1-6585,  by  which  the  ordinary 
refracted  ray  is  characterised.  The  less  refracted  ray, 
on  the  other  hand,  which  although  in  this  particular 
case  it  is  refracted  in  the  ordinary  manner,  must  be 
estimated  as  the  extraordinary  ray,  gives  the  ratio  of 
refraction  1*48654.  It  follows  from  this  that  the  extra- 
ordinary ray  is  propagated  in  a  plane  at  right  angles  to 
the  axis  of  the  crystal  with  a  velocity  of  1  :  1-48654,  or 
0'673,  whilst  the  velocity  of  the  ordinary  ray  is  only 
0-603. 

As  the  two  rays  obey  the  ordinary  laws  of  refrac- 
tion, the    construction  can  be  applied  to  them  from 
which  we  deduced  (§  98,  fig.  138)  the  law  of  refraction 
itself.     If,  namely,  two  circles  be  described  around  the 
point  of  incidence,  a,  with  the  radii  0-603  and  0-673 
(fig.  157),  these  will  represent  the  contours  of  the  two 
elementary  waves  contained  in 
the   plane    at    right   angles  to 
the  axis,  which  have  sprea.l  from 
the  point  a  in  the  crystal  in  the 
time    in   which    the   light   has 
traversed    the    length    of    path 
represented  by  unity  in  the  air. 

Double  refraction.    First  case.  r  »  J 

It  a  o  be  any  ordinarily  retracted 
ray,  and  we  draw  to  the   point  o,  where  it   cuts  the 


DOUBLE  EEFEACTION. 


287 


first  circle,  a  tangent,  o  b,  which  strikes  the  surface 
of  the  crystal  MN  at  the  point  5,  we  find  the  corre- 
sponding extraordinary  ray  when  we  join  the  point  a 
with  the  point  e,  in  which  a  straight  line,  b  c,  drawn 
from  b9  touches  the  second  circle. 

From  this  construction,  the  results  of  which  agree 
in  all  points  with  observation,  it  follows  however  that 
the  apparently  simple  beam  which,  when  its  incidence 
was  normal,  was  seen  to  leave  the  crystal,  really  con- 
sists of  two  fasciculi  which  have  traversed  the  crystal 
in  the  same  direction,  but  with  different  velocities. 

1 26.  If  now  the  cube  of  Iceland  spar  be  so  placed 
that  its  axis  is  at  right  angles  to  the  incident  rays, 
a  single  beam  is  seen  to  emerge  from  the  opposite 
surface  as  a  continuation  of  the  incident  rays ;  and 
if  the  crystal  be  now,  as  before,  slowly  rotated  round 
the  axis  so  that  the  incident  rays  constantly  strike 
its  anterior  surface  more  and  more  obliquely,  double 
refraction  is  observed  to  occur,  both  rays  remaining 
always  in  the  horizontal  plane  of  incidence.  Thus  the 
ordinary  ray,  as  might  be  expected,  behaves  itself 
exactly  as  in  the  former  case,  but  the  less  refracted 
extraordinary  ray  now  no  longer  follows  Snellius'  law 
of  refraction.  If  we  would  construct 
it  by  a  proceeding  similar  to  the 
foregoing,  we  must,  as  Huyghens 
has  shown,  instead  of  the  second 
circle  draw  an  ellipse  the  half  of 
the  major  axis  of  which,  a  p,  is  at 
right  angles  to  the  axis  of  the  crys- 
tal, and  is  equal  to  0-673,  but  the 

half  of  the  minor  axis  of  which,  an,  is  in  the  direction 
of  the  axis  of  the  crystal  and  is  equal  to  0-603  (fig.  158). 

20 


FIG.  158. 


Double  refraction.    Second 


288 


OPTICS. 


In  the  plane  of  incidence  parallel  to  the  axis  of  the 
crystal  the  contour  of  the  elementary  waves  correspond- 
ing to  the  extraordinarily  refracted  rays  is  represented 
by  this  ellipse,  which  touches  the  circular  contour  of 
the  ordinary  waves  at  the  terminal  points  of  its  diameter 
which  is  parallel  to  the  axis  of  the  crystal. 

The  same  ellipse  in  combination  with  the  circle 
included  in  it  also  serves  for  the  determination  of  the 
two  refracted  rays,  when  the  incident  rays  strike  at  any 
given  angle  of  incidence  upon  the  terminal  surfaces  of 
the  cube  which  are  at  right  angles  to  the  axis  of  the 
crystal,  except  that  now  the  small  axis,  a  m,  of  the  ellipse 
is  at  right  angles  to  the  surface  of  entrance,  MN  (fig. 
159).  When  the  light  enters  vertically  it  may  also  be 
observed  in  this  third  position  of  the  crystal,  as  in  the 
two  first,  that  only  a  single  ray  leaves  the  crystal  as 
continuation  of  the  incident  one ;  in  the  two  first  cases, 
however,  this  beam  is  only  apparently  simple,  being  in 
fact  composed  of  two  beams,  propagating  themselves  in 

the  same  direction  with  different 
velocities ;  whilst  in  the  case 
where  it  has  traversed  the  cube 
in  the  direction  of  the  crystalline 
axis,  it  is  really  simple,  because 
in  this  direction  the  rapidity 
of  propagation  am  =  0*603,  is 
the  same  for  the  extraordinary 
as  for  the  ordinary  ray  (fig.  159). 

Rays  which  pursue  a  course  parallel  to  the  axis  of 
the  crystal  do  not  therefore  undergo  any  refraction, 
whilst  in  every  other  direction  two  rays  are  propa- 
gated with  different  velocities.  On  account  of  this 
behaviour  the  axis  of  the  crystal  is  also  named  the 


FIG.  159. 


Double  refraction.    Third  case. 


DOUBLE  REFEACTION.  289 

optic  axis.  Every  plane  passing  through  the  optic  axis, 
or  parallel  with  it,  is  termed  a  principal  section.  Thus, 
for  example,  the  planes  of  the  figs,  158  and  159  are 
principal  planes,  because  they  contain  the  principal 
axis  within  them.  All  principal  sections  behave  in  ex- 
actly the  same  manner  in  reference  to  light. 

127.  A  view  of  the  double-shelled  elementary  wave 
which  spreads  out  from  every  point  of  a  crystal  of  Ice- 
land spar  struck  by  light,  in  consequence  of  the  two 
velocities  of  propagation,  is  obtained  by  combining  the 
contours  represented  in  figs.  157,  158,  and  159  in  an 
easily  intelligible  model  (fig.  160).  Since  the  ordi- 
nary rays  are  propagated  in  all 
directions  with  the  equal  velo- 
city of  0*603,  their  wave-surface 
is  obviously  a  sphere  with  a 
radius  of  0*603.  The  wave-sur- 
face of  the  extraordinary  rays 
exhibits,  as  we  know,  in  every 
principal  section,  the  same  ellip- 
tical contour,  ZXZ',  ZYZ',  the 

n        i   •    -i  •  Wave-surface  of  a  negative 

minor    aXIS    Of    Which    IS    COinCl-  uniaxial  crystal! 

dent  with  the  diameter  ZZ'  of 

the  sphere  that  is  parallel  with  the  optic  axis.  It  must 
therefore  be  represented  as  a  spheroid  flattened  in  the 
direction  of  the  optic  axis,  but  which  everywhere  in- 
cludes the  spherical  waves  of  the  ordinary  rays,  and 
only  touches  the  optic  axis  in  the  terminal  points  Z  and 
Z' '.  Whilst  the  axis  OZ  of  the  spheroid  equals  the 
radius  of  the  sphere  0-603,  the  radius  of  its  equator 
(OX=OY=OX')  amounts  to  0-673. 

With  the  aid  of  these  two-shelled  wave- surfaces  the 
two  refracted  rays  corresponding  to  any  incident  ray 


290 


OPTICS. 


FIG.  161 


B 


Huyghens'  construction  of 
double  refraction. 


may  always  be  determined  by  a  proceeding  which  is 
exactly  similar  to  that  applied  to  ordinary  refraction  in 
fig.  138.     Fig.  161,  which  likewise  makes  it  apparent 
upon  the   construction  given  by 
Huyghens  for  the  case  where  the 
optic   axis   lies   in    the  plane  of 
incidence,    but  obliquely   to   the 
surface  of  the  crystal,  requires  np 
further  explanation. 

128.  The  circumstance  that  the 
axis  of  symmetry  of  the  crystal- 
line form  is  also  coincidently  the 
axis  of  symmetry  in  relation  to  the 
propagation  of  rays  of  light,  sug- 
gests that  the  cause  of  double  refraction  of  Iceland 
spar  is  to  be  sought  for  in  its  special  properties  as  a 
crystal. 

Every  crystal  of  Iceland  spar  is  capable  of  cleavage 
parallel  to  the  surfaces  of  its  rhombohedric  fundamental 
form  (fig.  156,  a)  so  that  it  may  be  easily  broken  up 
into  smaller  and  still  smaller  fragments,  the  surfaces 
of  which  constantly  maintain  the  same  parallel  posi- 
tion. These  facts  prove  that  the  crystalline  form  is 
only  the  external  expression  of  regular  internal  struc- 
ture, which  there  can  be  no  doubt  is  caused  by  a  certain 
orderly  disposition  of  the  molecules. 

All  known  crystals  can  be  arranged  in  six  great 
divisions  or  systems,  in  accordance  with  the  laws  which 
govern  the  grouping  of  their  molecules.  In  the  crys- 
tals of  the  regular  system,  the  fundamental  form  of 
which  is  the  cube,  we  find  constantly  three  planes  at 
right  angles  to  each  other  (for  example,  the  three 
ed^es  that  meet  at  any  angle  of  the  cube),  which  are 


DOUBLE  KEFKACTION.  291 

completely  similar  to  one  another.  Sucli  crystals,  like 
those  of  fluor  spar  and  rock  salt,  exhibit  no  double 
refraction ;  they  refract  light  in  the  same  way  as  non- 
crystalline  bodies,  glass  and  fluids. 

Two  other  systems  of  crystals,  the  pyramidal  (das 
yuadratische) ,  and  the  rhombohedral  (das  hexagonale) 
possess  one  axis  of  symmetry  developed  beyond  the 
others.  All  the  crystals  belonging  to  these  systems 
are  doubly  retracting.  Two  rays  are  propagated  in 
them  in  different  directions,  an  ordinarily  and  an  extra- 
ordinarily refracted  ray.  Double  refraction  is  absent 
only  in  the  direction  of  the  axis  itself,  which  is  on 
this  account  named  the  optic  axis.  If  the  extraor- 
dinary rays  have  a  greater  velocity  than  the  ordinary, 
the  wave-shell  corresponding  to  them  has  the  form  of  a 
flattened  spheroid  which  invests  circularly  the  spherical 
wave  of  the  ordinary  rays.  Crystals  like  Iceland  spar, 
nitrate  of  soda,  and  others,  in  which  this  is  the  case, 
are  termed  negative.  Those  crystals  are  called  positive 
in  which,  as  in  quartz,  the  ordinary  rays  possess  the 
greatest  velocity.  In  these  the  wave-shell  of  the  extra- 
ordinary rays  is  represented  by  a  spheroid  prolonged  in 
the  direction  of  the  optic  axis,  which  is  everywhere  sur- 
rounded by  the  spherical  ordinary  wave,  and  is  only  in 
contact  with  it  at  the  two  extremities  of  the  optic  axis. 

The  crystals  of  the  three  remaining  systems,  the 
right  and  oblique  prismatic,  and  the  anorthic  (rhombischen, 
klinorhombischen  und  klinorhomboidischen)  are  also 
doubly  refracting,  but  neither  of  the  two  refracted  rays — 
neither  the  retarded  one  nor  the  more  swiftly  pro- 
pagated one, — obeys  in  general  the  ordinary  law  of 
refraction.  In  each  of  these  crystals  there  are  two  axes 
without  double  refraction,  which  maybe  called  the  optic 


292  OPTICS. 

axes.  These  crystals  are  therefore  termed  biaxially 
doubly  refracting,  in  order  to  distinguish  them  from  the 
two  preceding  uniaxially  doubly  refracting  systems.  The 
wave-surfaces  of  the  biaxial  crystals  consist  also  of  two 
shells,  of  which  one  is  enveloped  by  the  other  in  such 
a  manner  that  the  two  are  connected  with  each  other 
at  four  points  corresponding  to  the  terminal  points  of 
the  two  optic  axes.  With  the  aid  of  these  wave-sur- 
faces the  direction  of  the  two  refracted  rays  car  be 
determined  in  a  similar  way  in  biaxial  crystals  as  in 
fig.  161  for  uniaxial  crystals.* 

*   [It  must  be  observed  that  in  this  case  the  surfaces  are  not  spheroids 
but  surfaces  of  the  fourth  order. — TB.] 


CHAPTER  XXTT. 

POLARISATION    OF    LIGHT. 

129.  A  BEAM  of  solar  rays  is  constantly  split  into 
two  beams  of  equal  brilliancy  by  a  crystal  of  Iceland 
spar,  in  whatever  way  this  may  be  rotated  round  the 
axis  of  the  incident  rays.  When  Huyghens  allowed 
these  two  rays  to  fall  upon  a  second  crystal  of  Iceland 
spar,  he  observed  to  his  surprise  that  each  was  broken 
up  into  two  rays  of  unequal  brilliancy,  the  relative 
brightness  of  which  depended  on  the  position  of  the 
crystal,  whilst  there  were  two  positions  in  which  no 
double  refraction  occurred.  From  this  phenomenon  he 
rightly  concluded  that  both  of  the  rays  refracted  through 
a  crystal  of  Iceland  spar  acquired  peculiar  properties, 
by  which  it  was  distinguishable  from  direct  solar  light. 
In  order  to  distinguish  conveniently  one  of  the  two 
refracted  rays  from  the  other,  a  natural  rhombohedric 
crystal  of  Iceland  spar  may  be  FIG.  102. 

employed  (fig.  162,  A),  which 
is  fastened  by  means  of  a  cork 
ring  in  a  mefyil  tube.  The 
tube  is  closed  at  both  ends  by 
a  cover  perforated  at  its  centre 

Two  rhombohedra  of  Iceland  spar. 

by  the  round  apertures  a  and 

a'.     A  second  exactly  similar  rhombohedron  of  Iceland 

spar  is  attached  to  a  tube  (B),  with  a  similar  opening 


294  OPTICS. 

at  both  ends.  If  the  tubes  be  arranged  in  such  a 
manner  behind  each  other  that  their  axes  are  hori- 
zontal, and  a  beam  of  parallel  solar  rays  be  allowed 
to  enter  the  aperture  a  in  that  direction,  it  will  be  seen 
that  this,  on  account  of  its  falling  perpendicularly 
upon  the  anterior  surface  of  the  first  crystal  of  Iceland 
spar,  is  split  (as  seen  in  fig.  154),  into  two  rays,  of 
which  only  the  ordinarily  refracted  one  emerges  from 
the  aperture  a',  and  reaches  the  second  crystal.  In 
this  position  the  principal  planes  of  the  two  crystals 
running  through  the  ray  a  of  and  the  optic  axis  (the 
direction  of  which  is  indicated  by  the  shading),  lie  in 
one  and  the  same  horizontal  plane,  namely,  in  the 
plane  of  the  drawing. 

In.  this  parallel  position  of  the  principal  planes,  the 
ordinarily  refracted  ray  emerging  from  the  first  crystal 
does  not  undergo  double  refraction  afresh  in  the  second 
crystal,  but  traverses  it  simply  as  an  ordinarily  refracted 
ray,  without  materially  diminishing  in  brightness :  as 
soon  however  as  the  second  tube  is  rotated  a  little  either 
to  the  right  or  left,  double  refraction  takes  place,  and  the 
extraordinarily  as  well  as  the  ordinarily  refracted  spot 
of  light  appears  upon  the  screen.  As  it  is  turned  further 
and  further,  the  extraordinary  ray,  which  is  at  first  only 
faint,  continually  gains  in  brightness,  whilst  the  ordi- 
nary ray  becomes  proportionally  fainter  till  both  rays 
are  of  equal  brightness,  which  occurs  when  the  angle 
between  the  two  principal  planes  of  cleava  ge  is  45°.  On 
turning  it  still  further  the  brightness  of  the  ordinary 
ray  progressively  diminishes,  and  that  of  the  extraor- 
dinary ray  augments,  till  ultimately,  when  the  prin- 
cipal planes  of  section  are  placed  vertically,  or  at  right 
angles  to  each  other,  the  former  has  completely  dis- 


IOLAEISATION   OF  LIGHT.  295 

ft.ppeared,  whilst  the  latter  alone  remains  shining  with 
the  full  strength  of  the  raj  falling  on  the  crystal  B. 
The  ordinary  ray  again  begins  to  appear  as  the  rotation 
is  continued,  and  progressively  gains  in  brilliancy  with 
the  coincident  and  increasing  faintness  of  the  extraordi- 
nary ray  until,  after  rotation  to  the  extent  of  two  right 
angles,  the  principal  sections  of  the  two  crystals  again 
coincide,  when,  as  at  first,  the  ordinary  ray  is  alone 
present  in  its  original  brilliancy.  The  same  series  of 
phenomena  are  repeated  when  by  further  turning  the 
second  crystal  is  rotated  through  two  right  angles,  till 
it  arrives  at  the  position  which  it  originally  had.  The 
ordinarily  refracted  ray  emerging  from  the  first  crystal, 
the  principal  section  of  which  is  horizontal,  thus  gives 
rise  either  to  an  ordinary  ray  only,  or  to  an  extra- 
ordinary ray  only,  according  to  whether  the  principal 
section  of  the;  second  crystal  is  parallel,  or  at  right 
angles  to  it.  and  the  double  refraction  which  it  un- 
dergoes in  other  positions  takes  place  symmetrically  on 
both  sides  of  the  horizontal  and  of  the  vertical  plane. 

If  every  ray  had  the  same  properties  around  its  axis 
of  movement,  it  would  always  produce  the  same  pheno- 
mena whatever  might  be  the  direction  in  which  the 
second  crystal  of  Iceland  spar  was  turned.  Its  actual 
behaviour  however  shows  clearly  that  its  upper  and  lower 
sides  are  different  from  its  right  and  left  sides.  Such  n 
a  ray  possessing  different  sides  is  said  to  be  polarised. 

1 30.  The  knowledge  of  the  fact  that  there  are  rays 
of  light  with  different  sides,  constitutes  an  important 
step  in  advance  in  our  enquiries  into  the  nature  of  the 
undulations  of  light.  Hitherto  we  have  only  known 
that  the  particles  of  aether  arranged  serially  in  the 
direction  of  a  ray  of  light  performed  to  and  fro  move- 


296  OPTICS. 

ments,  but  in  regard  to  whether  the  direction  of  these 
vibrations  takes  place  in  the  direction  pursued  by  the  ray 
itself,  or  forms  an  angle  with  it,  the  phenomena  of  light 
already  considered  afford  no  clue.  However  oblique  to 
the  direction  of  the  ray  the  rectilinear  vibration  of  an 
sether  particle  may  be,  we  may,  in  accordance  with  the 
general  laws  of  motion,  regard  it  as  composed  of  two 
vibrations,  of  which  one,  the  longitudinal  vibration, 
takes  place  in  the  direction  of  the  ray,  whilst  the  other, 
the  transverse  vibration,  is  at  right  angles  to  the  ray. 
Consequently  in  regard  to  the  direction  of  the  vibra- 
tions in  any  ray  of  light,  we  have  only  the  choice  of 
three  possibilities  :  they  may  be  exclusively  longitudinal 
vibrations,  exclusively  transverse  vibrations,  or  coin- 
cidently  longitudinal  and  transverse  vibrations. 

A  ray  of  light  which  only  presents  longitudinal  vi- 
I  brations  must  exhibit  everywhere  the  same  characters 
around  its  line  of  propagation.  This  view  therefore, 
since  it  is  incapable  of  explaining  the  later ulity  of  the 
polarised  ray,  must  be  unconditionally  thrown  aside. 
The  phenomena  of  polarisation,  on  the  other  hand,  can 
be  at  once  explained  if  it  be  admitted  that  transverse 
vibrations  are  present.  For  if  we  suppose  that  in  a 
horizontal  ray  of  ligfht,  of  ~b  (fig.  162),  the  transverse 
vibrations  only  take  place  vertically  upward  and  down- 
ward, but  not  sideways,  its  upper  and  lower  side, 
towards  which  its  vibrations  are  alternately  directed,, 
must  obviously  be  different  from  its  right  and  left 
side. 

If  now  in  the  ray  of  light,  of  b,  longitudinal  vibrations 
as  well  as  transverse  be  present,  they  must  pass  through 
the  second  in  the  same  way  as  they  traverse  the  first 
crystal,  whatever  may  be  the  position  given  to  the  latter. 


POLARISATION   OF   LIGHT.  297 

But  we  hare  seen,  however,  that  when  the  crystals 
are  placed  with  their  principal  planes  at  right  angles 
with  each  other  the  ordinary  refracted  ray  disappears, 
and  it  may  easily  be  demonstrated  that  at  that  spot  of 
the  screen  where  it  ought  to  fall,  not  only  is  there  no 
light  but  no  heat,  and  no  fluorescent  action ;  the  fact 
that  at  this  spot  where  the  longitudinal  vibrations 
in  case  of  their  existence  must  necessarily  fall,  none 
of  those  actions  occur  which  we  now  know  to  be 
characteristic  of  the  aether  waves,  is  most  readily 
explicable  on  the  assumption  that  in  a  polarised  ray 
of  light  there  are  no  longitudinal,  but  only  transverse 
vibrations. 

Eig.  163  represents  consequently  a  polarised  ray  ; 
the  plane  in  which  its  transverse  vibrations  take  place, 
the  plane  of  the  paper  on  which  the  figure  is  drawn,  is 
called  the  plane  of  vibration.  If  a  second  plane  be  carried 
across  the  ray  at  right  angles  to  the  plane  of  vibration, 
the  ray  behaves  itself  symmetrically  in  reference  to 
these  two  planes. 

Experiment  tells  us  that  the  refracted  ray  emerging 
from  the  first  crystal  of  Iceland  spar  (the  principal 
section  of  which  is  horizontal),  is  symmetrical  in  rela- 
tion to  planes  carried  through  it  in  a  horizontal  and  a 
vertical  direction,  but  it  does  not  tell  us  which  of  these 
two  planes  is  the  plane  of  vibration ;  and  as  othei 
experiments  directed  to  the  solution  of  this  question 
have  not  hitherto  enabled  us  to  give  a  decisive  reply, 
we  may  accept  whichever  of  the  two  planes  we  please 
as  the  plane  of  vibration.  We  prefer  the  vertical,  that 
is  to  say,  we  admit  that  the  vibrations  of  the  ordinarily 
refracted  ray  are  vertical  or  at  right  angles  to  the 
principal  section  of  the  crystal. 


298  OPTICS. 

131.  And  now  let  the  aperture  a'  be  made  in  a 
small  slide  which  can  easily  be  placed  in  such  a  position 
that  the  extraordinary  ray  can  alone  emerge  from  the 
tube.  If  this  be  now  examined  in  the  same  way  as 
before  by  means  of  the  second  crystal,  we  see  upon  the 
screen  when  the  principal  planes  are  parallel  the  ordi- 
nary, and  when  they  decussate  at  right  angles  the 

FIG.  163. 


Polarised  ray  of  light. 

extraordinary,  ray.  The  extraordinary  ray  proceeding 
from  the  first  crystal  at  once  demonstrates  itself  to  be 
polarised,  and  indeed  polarised  at  right  angles  to  the 
ordinary  ray  ;  that  is,  if  we  regard  the  vibrations  of  the 
ordinary  ray  as  being  at  right  angles  to  the  principal 
plane,  and  thus  the  vibrations  of  the  extraordinary  ray  are, 
in  the  plane  of  the  principal  plane  of  cleavage  itself. 

132.  The  two  polarised  rays  emerging  from  the 
Iceland  spar  contain,  we  must  conclude,  no  longi- 
tudinal vibrations.  The  question  arises  whether  the 
longitudinal  vibrations  are  lost  in  their  passage  through 
the  crystal  from  some  absorptive  action  it  possesses,  or 
whether  they  are  already  absent  in  the  direct  rays  of 
the  sun.  To  obtain  some  data  for  an  answer  to  this 
question,  the  first  crystal,  A,  must  alone  be  used,  and  the 
little  cover  a'  must  be  removed  from  its  frame.  The 
two  light  spots  belonging  to  the  ordinarily  and  to  the 
extraordinarily  refracted  rays  then  reappear  upon  the 
screen,  and  keep  their  original  brilliancy  in  whatever 


POLARISATION   OF  LIGHT.  299 

direction  the  crystal  is  turned.  If  the  cover  a  be  now 
removed,  and  its  place  supplied  by  another  having  a 
l?rger  aperture,  the  light  spots  become  correspondingly 
larger,  though  the  space  between  their  middle  points 
is  not  changed;  they  are  so  large  indeed  that  they 
partially  overlap  each  other.  In  the  part  common  to 
both,  where,  namely,  the  transverse  vibrations  of  the 
ordinary  mingle  with  those  of  the  extraordinary  rays,  a 
degree  of  brightness  is  produced  upon  the  screen  which 
is  not  materially  less  than  that  of  the  direct  light  of  the 
sun  after  passing  through  the  same  aperture  without 
the  intervention  of  the  crystal  of  Iceland  spar.* 

If  therefore  longitudinal  vibrations  be  present  in  the 
direct  solar  light,  they  nevertheless  produce  no  obvious 
effect,  or  rather  none  of  those  effects  which  we  have 
learnt  to  ascribe  to  the  sether  waves  proper.  The  most 
probable  view  which  presents  itself  in  this  respect  is 
therefore  that  the  unpolarised  natural  light,  like  the 
polarised,  has  no  longitudinal  vibrations,  but  consists 
only  of  transverse  vibi  ations.  This  view  receives  essential 
support  from  the  circumstance  that  all  the  known  phe- 
nomena of  light  are  only  perfectly  explicable  on  the 
assumption  that  light  consists  exclusively  of  transverse 
vibrations. f 

*  The  slight  diminution  in  the  intensity  of  the  light  which  may  be 
demonstrated  in  the  light  which  has  traversed  the  Iceland  spar,  is  fully 
accounted  for  by  the  two  reflexions  from  the  anterior  and  posterior  surfaces 
of  the  crystal. 

f  It  results  from  the  laws  of  wave-movement  that  longitudinal 
vibrations,  if  present  at  all,  must  be  propagated  with  unequal  and  greater 
velocity  than  the  transverse  vibrations,  and  consequently  would  already  far 
outstrip  them  at  even  a  small  distance  from  the  source  of  light.  Since, 
moreover,  the  dispersion  of  colour  can  only  be  explained  upon  the  ad- 
mission of  transverse  vibrations,  we  are  perfectly  justified  on  these  theo- 
retical grounds  in  holding  these  last  only  to  be  luminous  vibrations. 


300  OPTICS. 


.  If  the  portion  of  light  emerging  from  the 
Iceland  spar  common  to  the  two  beams  be  somewhat 
more  closely  examined,  for  example  by  allowing  it  to 
fall  upon  the  second  crystal,  it  will  be  found  that  it 
behaves  just  like  natural  non-polarised  light.  By  Hie 
combination  of  these  two  rays  of  equal  brilliancy,  polarised 
at  right  angles  to  each  other,  ordinary  natural  light  is  pro- 
duced, and  conversely,  every  ray  of  natural  light  may 
be  regarded  as  being  composed  of  two  equally  bright 
rays  polarised  at  right  angles  to  each  other.  It  is  con- 
sequently of  no  importance  what  direction  we  assume 
for  the  vibrations  of  the  one  ray,  if  only  it  be  admitted 
that  those  of  the  other  equally  bright  ray  are  perpen- 
dicular to  them.  For  the  everywhere  similar  vibrations 
of  the  part  common  to  the  two  beams  present  no  varia- 
tion in  whatever  manner  the  crystal  is  rotated  around 
the  axis  of  the  draw  tube  ;  in  every  position  the  two- 
sidedness  of  the  one  ray  is  completely  neutralised  by 
the  opposite  two-sidedness  of  the  other. 

Two  rays  polarised  at  right  angles  to  each  other 
produce,  as  Fresnel  and  Arago  have  demonstrated  by 
experiment,  no  phenomena  of  interference  ;  they  pro- 
duce on  the  contrary  (whatever  may  be  their  difference 
of  path)  always  the  same  degree  of  illumination,  that, 
namely,  which  is  equal  to  the  sum  of  the  two  rays  in 
co-operation.  It  is  evident  in  fact  that  two  motions  at 
right  angles  to  one  another  cannot  neutralise  each 
other.  Two  polarised  rays  however,  having  a  common 
source,  that  is  to  say,  which  originate  in  one  and  the 
same  polarised  ray,  may  clearly  do  so  if  their  planes  of 
vibration  coincide.  Two  rays  of  natural  light  which 
proceed  from  the  same  source  are  therefore  always 
capable  of  interference,  for  if  either  of  them  be  con- 


POLARISATION   OF  LIGHT.  301 

ceived  to  be  broken  up  into  its  two  polarised  con- 
stituents travelling  in  the  two  planes  at  right  angles  to 
eaoii  other,  then  those  pairs  of  these  four  rays  which 
have  a  common  plane  of  vibration  will  act  upon  each 
other,  and  according  to  the  amount  of  their  common 
difference  of  path,  coincidently  abolish  or  strengthen 
each  other. 

134.  The  velocity  with  which  a  vibratory  movement 
is  propagated  in  an  elastic  medium  is  not  simply 
dependent  upon  the  density  of  the  medium,  but  also 
upon  the  elasticity  which  this  possesses  in  the 
direction  of  the  vibration.  In  free  space,  in  air,  in 
water,  in  glass,  and  speaking  generally  in  all  simply 
refracting  bodies,  the  elasticity  of  the  aether  is  in  all 
directions  the  same.  The  two  constituents  of  a  natural 
ray  of  light  vibrating  at  right  angles  to  each  other 
propagate  themselves  therefore  always  with  equal  velo- 
city, and  remain  throughout  the  whole  of  their  path 
capable  of  being  reunited  to  form  a  natural  ray  of  light. 

The  mechanical  disposition  of  the  molecules  in  a 
doubly  refracting  crystal  is  the  cause  of  its  physical 
properties  differing  in  different  directions.  In  a 
crystal  of  this  kind  it  may  be  demonstrated  that  heat 
is  propagated  with  unequal  velocity  in  different  direc- 
tions, that  it  expands  unequally  when  heated,  and  that 
its  various  surfaces  show  different  degrees  of  resistance 
to  cleavage,  and  to  the  chemical  action  of  various 
reagents.  The  view  therefore  appears  to  be  justified 
that  the  elasticity  of  the  sether  contained  between  the 
molecules  of  the  crystal  is  different  in  different  direc- 
tions. In  crystals  with  an  axis  of  symmetry  for 
example,  we  must  admit  that  the  elasticity  around  and 
at  right  angles  to  the  axis  is  of  one  kind,  whilst  it  is 


302  OPTICS. 

different  in  the  direction  of  the  axis  itself,  and  con- 
tinually changes  in  passing  from  this  direction  into  the 
former. 

This  theory  renders  it  intelligible  why  the  two  com- 
ponents of  a  ray  of  natural  light  vibrating  at  right 
angles  to  each  other  in  traversing  a  crystal  of  this  kind, 
break  up  into  two  polarised  rays  which  are  propagated 
with  unequal  velocity.  It  is  only  when  the  ray  of  light 
follows  the  optic  axis  itself  that  its  two  components 
vibrate  at  right  angles  to  this,  and  call  into  play  equal 
elastic  forces ;  they  are  hence  propagated  with  equal 
velocity,  and  continue  in  their  further  path  united  to 
Form  a  ray  of  natural  light. 


CHAPTEE  XXIH. 

POLARISING  APPARATUS. 

135.  IN  double  refraction,  which  breaks  up  every 
beam  of  natural  light  into  two  polarised  rays,  we  possess 
an  excellent  means  of  procuring  polarised  light.  But 
inasmuch  as  the  two  beams  when  reunited  are  capable 
of  again  forming  natural  light,  it  is  necessary  to  devise 
some  method  of  setting  one  of  them  aside.  This,  for 
example,  can  be  done  by  fixing  a  rhombohedric  crystal 
of  fluor  spar,  as  in  fig.  162,  A,  in  a  tube  which  is 
closed  at  its  extremities  with  appropriate  caps.  In 
order  that  the  ordinarily  refracted  ray  may  emerge 
separately  from  the  tube,  the  diameter  of  each  of  the 
two  openings,  a  and  a',  in  the  middle  of  the  caps  should 
amount  to  about  only  the  tenth  part  of  the  thickness  of 
the  fluor  spar.  If  these  limits  be  overstepped,  a  portion 
of  the  extraordinary  ray  will  also  pass  out  through  the 
opening  a',  and  we  shall  no  longer  be  dealing  with 
completely  polarised  light.  Applied  in  this  way  as  a 
'  polariser,'  even  a  very  large  crystal  of  Iceland  spar  can 
only  give  a  very  thin  beam  of  polarised  light.  In  order 
to  employ  this  valuable  material  to  greater  advantage, 
Nicol  conceived  the  following  ingenious  idea.  He  ob- 
tained, by  cleavage  from  a  crystal,  a  four-sided  column 
with  rhombic  terminal  surfaces,  so  that  the  form  of  the 
chief  section  through  its  obtuse  lateral  angles  ay  and 


304 


OPTICS. 


ed,  had  the  form  of  fig.  164.  The  prism  is  now  to  be 
sawn  asunder  along  the  line  b  c,  that  is,  in  the  direction 
from  one  obtuse  angle  e  to  the  other,  at 
right  angles  to  the  principal  cleavage 
plane,  and  the  two  cut  surfaces,  after 
they  have  been  polished,  are  to  be  again 
cemented  together  in  their  original  po- 
sition by  means  of  Canada  balsam. 

If  a  ray  of  natural  light,  m  n,  fall  on 
the  rhombic  anterior  surface,  a  e,  of  the 
Nicol's  prism,"*  it  breaks  up  into  an 
ordinary  refracted  ray,  np,  and  an  ex- 
traordinarily refracted  one,  n  o.  The 
former,  the  index  of  refraction  of  which 
(1-6585),  is  greater  than  that  of  Canada 
balsam  (1*53),  strikes  so  obliquely  upon 
the  surface  of  the  cement  that  it  can- 
not penetrate  it,  but  undergoes  complete  reflexion. 
The  extraordinary  ray,  on  the  other  hand,  which  pro- 
pagates itself  with  greater  rapidity  in  Iceland  spar  than 
in  Canada  balsam,  penetrates  the  latter  under  all  cir- 
cumstances, and  leaves  the  posterior  s.urface,  d  g,  as  a 
completel}7  polarised  ray,  r  s,  the  vibrations  of  which, 
in  my  opinion,  are  parallel  to  the  principal  section, 
aecfg. 

A.  NicoFs  prism  thus  permits  only  those  vibrations 
to  traverse  it  that  are  parallel  to  its  principal  plane  of 
cleavage,  whilst  it  is  completely  opaque  for  rays  which 
are  at  right  angles  to  the  principal  plane.  For  the  sake 
of  convenience  it  is  fixed  in  a  metal  frame,  which  is 
not  usually  provided  with  a  diaphragm,  for  all  the  rays 


*  Often  termed  for  the  sake  of  brevity  the  '  Nicol.' 


POLAEISING  APPARATUS.  305 

that  fall  parallel  upon  the  first  surface,  m  n,  issue  from 
the  second  as  a  completely  polarised  fasciculus  of  pa- 
rallel rays,  the  breadth  of  which  amounts  to  about  a 
third  of  the  length,  ag,  of  the  piece  of  spar  employed. 

The  Nicol's  prism,  as  well  as,  speaking  generally, 
every  '  polariser,'  can  also,  conversely,  be  made  use  of 
as  a  6  polariscope,'  that  is  to  say,  may  serve  as  a  means 
of  recognising  any  ray  of  light  as  being  polarised,  and 
determine  the  position  of  its  plane  of  vibration.  If 
for  example  natural  light  fall  upon  a  Nicol's  prism,  a 
polarised  beam  issues  from  it  which  maintains  con- 
stantly the  same  degree  of  brilliancy  in  whatever 
manner  the  Nicol's  prism  be  rotated  around  the  direc- 
tion of  the  incident  rays.  In  fact,  in  every  position  of 
the  Nicol's  prism,  half  the  incident  light  traverses  it 
as  polarised  light.  If  on  the  other  hand  polarised 
rays  be  allowed  to  fall  upon  a  Mcol's  prism,  they  are 
only  perfectly  transmitted  when  its  chief  section  is 
parallel  with  the  plane  of  vibration  of  the  incident 
rays ;  but  if  the  Nicol  be  rotated  out  of  this  position, 
the  transmitted  light  becomes  constantly  more  and 
more  faint,  and  ultimately  entirely  vanishes  when  the 
chief  section  of  the  Nicol  is  at  right  angles  to  the  plane 
of  vibration. 

136.  The  Nicol's  prism  may  now  be  applied  as  a 
polariscope  to  the  investigation  of  the  light  reflected 
from  a  plate  of  mirror-glass  which  has  not  been  sil- 
vered. A  beam  of  natural  light,  a  b,  is  allowed  to  fall 
upon  the  glass  plate  R  S  (fig.  165)  at  any  angle,  and 
is  reflected  towards  c.  If  the  Mcol's  prism  be  placed 
in  the  path  of  the  ray  b  c,  and  rotated  around  this  ray 
as  an  axis,  it  will  be  observed  that  the  transmitted 
light  is  sometimes  brighter,  sometimes  fainter,  though 


306  OPTICS. 

it  does  not  entirely  vanish  in  any  position  of  the  NicoPs 
prism.     The  light  reflected  from  the  glass  plate  is  con- 
sequently neither   natural   light,  nor   is  it  completely 
polarised.     Its  behaviour  is  ra- 
ther as  if  it  were  a  mixture  of 
natural  and  polarised  light,  and  it 
is  therefore  said  to  be  partially 
polarised.      The  Nicol,  in   what- 
f  ever  position  it  may  be  placed, 

Polarisation  by  reflexion.  allows  one  half  of  the  unpolar- 
ised  constituent  to  pass  through,  whilst  the  polarised 
constituent  is  extinguished  or  transmitted  according 
to  whether  the  principal  plane  of  the  Nicol  is  at  right 
angles  to,  or  parallel  with  its  vibrations.  Tn  order  to 
determine  the  plane  of  vibration  of  the  polarised  por- 
tion, it  is  only  necessary  to  place  the  Nicol  in  such  a 
position  that  the  transmitted  light  is  as  faint  and  feeble 
as  possible.  This  takes  place  when  the  principal 
cleavage  plane  of  the  Nicol  comes  to  lie  in  the  plane 
of  incidence,  a  b  c.  From  which  we  draw  the  conclusion, 
that  the  plane  of  vibration,  df  I  m,  of  the  polarised  light 
contained  in  the  reflected  beam,  is  at  right  angles  to  the 
plane  of  incidence,  ah  c. 

The  proportion  of  the  polarised  portion  to  the  non- 
polarised varies  with  the  angle  of  incidence.  With 
vertical  incidence  for  example,  the  reflected  beam  con- 
tains no  polarised  light,  but  if  the  angle  of  incidence 
amount  to  57°,  or  if  the  incident  rays  form  an  angle 
(abh)  of  .33^  with  the  glass  plate,  the  unpolarised  por- 
tion is  entirely  absent.  At  this  angle  of  incidence,  which 
is  known  as  the  polarisation  angle,  the  light  reflected 
from  the  glass  plate  undergoes  complete  polarisation, 
and  its  vibrations  take  place  at  right  angles  to  the 


POLARISING  APPARATUS. 


307 


FIG.  16fi. 


plane  of  incidence  (or  parallel,  df)  as  is  indicated  by 
the  wave-line  in  the  figure.  ^f 

1  137.  A  glass  plate  placed  at  this  angle,  since  it 
only  reflects  vibrations  at  right  angles 
,  to  the  plane  of  incidence,  thus  forms 
an  excellent '  polariser.'  Instead  of  ex- 
amining the  rays  reflected  from  it  by 
means  of  a  Nicol's  prism  they  may 
be  received  at  the  same  angle  on  a 
second  glass  plate  (fig.  166),  which  then 
P^ys  the  part  of  a  polar iscope.  If  the 
two  plates,  as  in  the  figure,  are  parallel 
to  each  other,  their  planes  of  incidence 
x  are  parallel,  and  the  ray  b  c,  the  vibra- 

tions of  which  are  at  right  angles  to  the  plane  of 
incidence  common  (to  both,  is  reflected  from  the  second 
plate  to  cd.  But  if  the  second  plate  be  rotated 
from  this  parallel  position  whilst  it  still  forms  the 
angle  33°  with  the  direction  of  the  ray  b  c,  the  light 
reflected  from  it  becomes  weaker 
and  weaker  till  it  entirely  dis- 
appears when  the  two  planes  of 
incidence  are  at  right  angles  to 
each  other.  For  in  this  crossed 
position  the  vibrations  of  the 
ray  be  lie  in  the  plane  of  incid- 
ence of  the  second  plate,  and 
are  not  reflected,  because  only 
those  vibrations  that  are  at  right 
angles  to  their  plane  of  incidence 
are  capable  of  reflexion.  In 
order  to  arrange  this  experiment  conveniently,  the 
apparatus  shown  in  fig.  167  may  be  employed.  To 


Blot's  polarising  apparatus. 


308  OPTICS. 

one  end  of  a  tube  blackened  in  its  inside  a  mirror 
of  black  glass,  D  B,  is  so  attached  that  it  forms  an 
angle  of  33°  with  the  axis  of  the  tube.  Rays  which 
run  parallel  to  the  axis  of  the  tube  from  D  to  0,  are 
reflected  at  the  mirror  under  the  angle  of  polarisation, 
and  are  therefore  completely  polarised.  A  second  black- 
ened mirror  is  attached  to  a  ring  at  the  other  end  of  the 
tube,  which  is  likewise  inclined  at  an  angle  of  33°  to  the 
axis  of  the  tube,  and  by  rotation  of  the  ring  can  be 
brought  into  the  different  positions  required  in  this  ex- 
periment. A  blackened  mirror  is  selected  in  order  to 
avoid  transmitted  unpolarised  light,  which  might  be 
mingled  with  the  light  polarised  by  reflexion.  Silvered 
mirrors  cannot  be  employed  as  polarisers,  because  they 
do  not  completely  polarise  the  reflected  light  under  any 
angle  of  incidence. 

Every  kind  of  apparatus  which,  like  that  just 
described,  constructed  by  Biot,  is  composed  of  two 
polarising  arrangements,  of  which  one  acts  as  polariser 
and  the  other  as  polariscope,  is  called  a  polarising  ap- 
paratus. The  apparatus  of  Norremberg,  shown  in 
fig.  168,  is  the  best  adapted  for  the  greater  number  of 
experiments.  A  transparent  plate  of  mirror- glass,  C  D, 
here  acts  as  a  polariser,  and  forms,  with  the  vertical 
axis,  n  c,  of  the  instrument  an  angle  of  33° ;  the  light 
incident  in  the  direction  m  n,  which  is  completely  po- 
larised, is  in  the  first  instance  deflected  vertically  down- 
wards, and  from  thence  it  i  5  reflected  vertically  upwards 
again  upon  itself  by  a,  mirror,  c,  fixed  in  the  foot  of  the 
instrument,  so  that  after  it  has  traversed  the  glass 
plate,  C  D,  it  can  reach  in  the  direction  of  the  axis  of 
the  apparatus  the  black  mirror,  (7  D',  acting  as  polari- 
scope. The  ring  i,  to  which  two  columns,  a'  and  &',  are 


POLARISING  APPAEATUS. 


309 


FIG.  ics. 


attached,  supporting  this  mirror,  revolves  within  a  fixed 
ring  K,  divided  into  degrees,  and  supported  by  the  rods 
a  and  b.  Tne  zero  of  the  di- 
visions of  the  fixed  ring  is  so 
arranged  that  when  the  indi- 
cator i  of  the  rotating  ring  is 
placed  upon  it,  the  plane  of 
incidence  of  the  mirror  (7  Df 
is  parallel  with  that  of  the 
glass  plate  C  1>.  In  the  pre- 
sent position  of  the  instru- 
ment, the  planes  of  incidence 
are  at  right  angles  (the  in- 
dicator standing  at  90°)  ;  the 
light  coining  from  below  is 
therefore  not  reflected  by  the 
mirror  (7  D' '. 

138.  Moreover  the  light 
transmitted  by  a  glass  plate 
at  an  acute  angle,  when  ex- 
amined with  a  Nicol's  prism 
is  found  to  be  partially  polar- 
ised, and  the  vibrations  of  the 
polarised  portion  are  con- 
stantly in  the  plane  of  inci- 
dence^ or  in  other  words  the 
transmitted  is  polarised  at  right  angles  to  the  reflected 
light.  As  Arago  has  shown,  the  quantities  of  light  po- 
larised at  right  angles  to  each  other  in  the  refracted 
and  in  reflected  rays  are  equal  to  each  other  at  every 
angle  of  incidence.  But  whilst  the  reflected  light  at  a 
determinate  angle  of  incidence,  namely,  at  the  polarising 
angle,  appears  to  be  completely  polarised,  some  nn- 


Nuremberg's  polarising  apparatus. 


810  OPTICS. 

polarised  is  mingled  with  the  transmitted  light ;  it  is 
always  only  partially  polarised,  whatever  may  be  the 
angle  selected. 

In  the  same  manner  a  nearly  complete  polarisation 
of  the  transmitted  rays  may  be  effected  if,  instead  of  a 
few,  a  sufficient  number  of  glass  plates  be  superimposed 
upon  each  other.  If  a  ray  of  natural  light  fall  upon 
such  a  series  of  plates  placed  at  the  polarising  angle, 
and  we  conceive  the  same  to  be  broken  up  into  its  two 
halves,  of  which  one  vibrates  in  the  plane  of  incidence 
and  the  other  at  right  angles  to  it,  the  former  half, 
because  on  account  of  the  direction  of  the  vibration  it 
is  incapable  of  reflexion,  is  transmitted  through  all 
the  laminae  almost  without  loss.  The  other  half,  on  the 
contrary,  undergoes  at  each  surface  a  partial  reflexion, 
and  owing  to  these  repeated  reflexions  becomes  so 
faint  as  to  be  no  longer  perceptible.  Of  those  rays  which 
are  presented  to  a  succession  of  glass  plates  of  this  kind 
at  the  polarising  angle,  only  such  are  transmitted,  to 
any  marked  extent,  as  vibrate  parallel  to  the  plane  of 
incidence,  and  the  plates  can  therefore  be  used  for  a 
polariser  as  well  as  for  a  polariscope. 

Fig.  169  shows  a  Norremberg's  polarising  apparatus, 
the  polariscope  of  which  is  the  glass  plate,  C  D.  The 
light  polarised  by  the  glass  plate  A  B,  is  extinguished 
when  the  plane  of  incidence  is  coincident  with  that  of 
the  series  of  plates,  CD.  This  arrangement  offers  this 
advantage,  that  the  visual  line  of  the  observer,  whilst 
the  polariscope  is  rotated,  can  remain  constantly  in  the 
direction  of  the  axis  of  the  instrument,  whereas  in  the 
instrument  represented  in  fig.  168,  the  eye  is  compelled 
to  follow  the  movements  of  the  blackened  mirror.  The 
same  object  can  also  be  more  conveniently  attained 


POLARISING  APPARATUS. 


311 


FIG.  169. 


when  the  generally  somewhat  expensive  NicoPs  prism 
is  applied  as  a  polari  scope. 

139.  After  Maius,  in  1810, 
had  discovered  the  polarisation 
of  light  reflected  and  refracted 
through  glass  plates,  he  showed 
further  that  almost  all  reflecting 
surfaces,  with  the  exception  of 
metallic  ones,  were  capable  of 
polarising  light,  but  that  the 
polarising  angle  at  which  this 
took  place  differed  for  different 
substances.  That,  for  example, 
required  in  the  case  of  Water  is 
53°;  for  Carbon  bisulphide  5i-° ; 
for  Flint-glass  60°.  From  these 
values  it  appears  that  the  po- 
larising angle  of  any  substance 
increases  with  its  refracting  power 
for  light.  Malus  was,  however, 
not  in  a  position  to  ascertain  this  relation,  and  its  dis- 
covery was  reserved  for  the  ingenuity  of  Brewster,  who, 
in  1815,  found,  that  the  polarising  angle  is  that  angle  of 
incidence  at  which  the  reflected,  forms  a  right  angle  with 
the  refracted  ray. 

This  law  supplies  an  additional  means  for  the  deter- 
mination of  the  index  of  refraction,  the  more  valuable 
since  it  can  be  used  in  the  case  of  substances  having 
only  a  small  degree  of  transparency,  and  to  which  the 
former  or  prismatic  method  (§  35)  is  not  applicable. 
For  just  as  by  means  of  Brewster's  law,  we  can  deduce 
the  polarising  angle  from  the  known  ratio  of  refrac- 


Norremberg's  polarising  appa- 
ratus with  glass  laminae. 


81 2  OPTICS. 

tion,  so,  conversely,  we  can  obtain  the  ratio  of  refraction 
from  the  polarising  angle. 

The  indices  of  refraction  of  Anthracite,  1*701 ;  Horn, 
1*565;  and  Menilite,  1*482,  given  in  the  tables,  have 
thus  been  ascertained  from  observing  the  polarising 
angle.  As  the  indices  of  refraction  of  the  different 
coloured  rays  are  unequal,  their  polarising  angle,  though 
perhaps  only  to  a  small  extent,  must  also  differ ;  white 
light  can  therefore  never  be  completely  polarised  by 
reflexion,  but  only  one  of  its  homogeneous  colours, 
whilst  the  rest  only  approximate  to  complete  polari- 
sation. 

The  undulatory  theory,  as  Fresnel  and  Cauchy  have 
shown,  also  gives  an  intelligible  and  satisfactory  ex- 
planation of  the  phenomena  of  polarisation  by  reflexion 
and  refraction.  From  the  law  of  conservation  of  energy, 
which  requires  that  the  energy  of  the  reflected  and  that 
of  the  refracted  wave  should  be  together  equal  to 
that  of  the  incident  wave,  as  well  as  from  the  condition 
that  the  amount  of  motion  at  the  line  of  junction  ot 
the  two  media  must  be  equal,  we  are  enabled  to  calcu- 
late the  nature  of  the  reflected  and  of  the  retracted 
rays.  From  such  a  calculation  the  laws  of  Arago 
(§  138)  and  of  Brewster  (§  139),  obtained  by  experiment, 
follow  directly,  and  in  all  other  respects  it  proves  to  be 
in  complete  unison  with  the  results  of  observation. 

140.  As  has  been  demonstrated,  the  colours  of  trans- 
parent bodies  originate  in  the  absorption  which  certain 
homogeneous  colours,  that  is  to  say,  rays  of  a  definite 
number  of  vibrations,  undergo  in  their  passage  through 
those  bodies.  In  the  case  of  coloured  doubly  refracting 
crystals  the  amount  of  absorption  is  dependent  not 
simply  on  the  number  of  vibrations  of  the  transmitted 


POLARISING   APPARATUS.  3J3 

rays,  but  also  upon  the  angle  which  the  direction  of 
their  vibrations  forms  with  the  optic  axis  of  the  crystal, 
a  circumstance  which  gives  rise  to  a  remarkable  pheno- 
menon which  may  now  be  investigated. 

Let  a  small  cube  of  Pennine,  a  mineral  belonging  to 
the  rhombohedral  system  of  crystals,  in  which  the  planes 
of  two  opposite  surfaces  are  at  right  angles  to  the  optic 
axis,  whilst  the  others  are  parallel  to  it,  be  selected. 
Tf  the  observer  look  through  the  cube  in  the  direction 
of  the  optic  axis,  it  appears  to  be  of  a  dark  bluish  green 

colour,  whilst  when  looked  at  from  the  sides  it  has  a 
7 

brown  colour.  This  peculiarity  is  called  dichroism. 
These  two  colours  will  be  seen  on  the  screen  if  the 
sun's  rays  be  transmitted  through  the  crystal  first  in 
one  direction  and  then  in  the  other.  The  bluish  green 
light  which  has  traversed  the  crystal  along  its  optic 
axis  contains  only  those  natural  rays  the  vibrations  of 
which  are  at  right  angles  to  the  optic  axis.  The  olive- 
green  light,  on  the  other  hand,  is  composed  of  ordinarily 
refracted  rays,  which  vibrate  at  right  angles,  and  of  ex- 
traordinarily refracted  rays,  which  vibrate  parallel  to  the 
axis.  These  two  constituents  may  easily  be  separated 
from  one  another  by  a  NicoPs  prism  placed  behind 
the  crystalline  cube.  For  if  the  principal  section  of 
the  Nicol's  prism  be  placed  at  right  angles  to  the  optic 
axis  of  the  cube  of  Pennine,  the  same  bluish  green  colour 
appears  upon  the  screen  which  was  previously  observed 
in  the  rays  that  had  traversed  the  crystal  in  the  direc- 
tion of  the  axis,  but  if  the  Nicol  be  placed  parallel  to 
the  optic  axis,  the  bright  spot  upon  the  screen  appears 
brownish  yellow.  The  rays  of  light  traversing  a  crystal 
of  Pennine  consequently  experience  an  amount  and  kind 
of  absorption  varying  according  to  whether  their  vibra- 


314 


OPTICS. 


FIG.  17(). 


tions  are  at  right  angles  to  or  parallel  with  the  axis  ;  in 
the  former  case  they  appear  bluish  green,  in  the  second 
brownish  yellow,  and  the  above-mentioned  brown  is  only 
the  mixture  of  these  two  colours. 

A   remarkable  inequality  in  the  power   of  absorp- 
tion  according   to   the    direction  of  the   vibrations  is 
shown  by  Tourmaline,  which  even  when  only  of  mode- 
rate thickness  completely  extinguishes  ordinary  rays. 
A  plate  of  Tourmaline,  cut  parallel  to  the 
optic   axis  of  the  crystal,   allows  therefore 
only  the  extraordinary  rays  vibrating  parallel 
to  the  axis  of  the  crystal  to  pass  through  it, 
and  can  therefore  act  as  a  polariser  as  well 
as  a  polariscope. 

A  combination  of  two  Tourmaline  plates, 
as  shown  in  fig.  170,  forming  the  so-called 
Tourmaline  forceps  or  tongs,  constitutes  the 
simplest  of  all  polarising  apparatus.  In  this, 
for  the  sake  of  convenience,  the  plates  are 
fastened  by  means  of  cork  discs  in  wire 
rings,  in  which  they  can  be  made  to  rotate. 
By  means  of  a  coiled  elastic  wire  they  can 
be  gently  pressed  together  so  that  any  object 
placed  between  them  which  is  required  to 
be  seen  with  polarised  light  is  held  as  if  by  a  pair  of 
tongs  or  forceps. 

If  the  plates  be  placed  in  such  a  position  that  their 
axes  are  parallel  (fig.  171),  the  light  of  the  sun  tra- 
verses them  just  as  it  would  through  a  single  plate  of 
the  same  thickness  as  the  two  together.  But  if  one  of 
the  plates  be  .rotated,  the  transmitted  light  becomes 
fainter  and  fainter,  till  when  the  axes  of  the  two  are  at 
right  angles  it  entirely  disappears. 


POLAKISING   APPAEATUS. 


315 


The  yellowish  brown  or  brownish  green  colour 
which  the  Tourmaline  communicates  to  transmitted 
light  seriously  interferes  with  its  applicability  as  a 


FIG.  171. 


FIG.  172. 


Tourmaline  plates  placed  parallel 
to  each  other. 


Tourmaline  plates  placed  at  right 
angles. 


polarising   apparatus,  for   which    its    simplicity    would 
otherwise  render  it  very  well  adapted. 


3 1 6  OPTICS. 


CHAPTEE   XXIV. 

INTERFERENCE  OWING  TO  DOUBLE  REFRACTION. 

141.  VERT  few  crystals  exhibit  the  phenomena  ot 
double  refraction,  so  distinctly  as  Iceland  spar;  in  mcst 
instances  there  is  so  small  a  difference  between  the  two 
velocities  of  propagation  that  the  splitting  or  decom- 
position of  an  incident  beam  into  two  fasciculi  of  rays 
can  only  be  perceived  when,  as  seldom  happens,  the 
crystals  can  be  obtained  of  considerable  thickness.  The 
circumstance,  however,  that  the  two  rays  resulting  from 
double  refraction  are  always  polarised,  renders  it  pos- 
sible to  recognise  even  the  slightest  amount  of  double 
refraction,  and  to  investigate  its  laws. 

With  this  object  in  view,  two  Nicol's  prisms,  ^and  B 
(fig.  173),  placed  horizontally  one  behind  the  other,  are 
F]G  173  employed  as  a  polarising  appa- 

ratus.    The  first,  the  principal 
cleavage  plane  of  which  is  ver- 
tical,  gives  a  parallel  beam  of 
vertically     vibrating    polarised 
rays  which  are  not  transmitted 
by    the    second,    the    principal 
TWO  Nicoi-B  prisms  enjoyed  as  a    cleavage  plane  of  which  is  hori- 
poiamiMg  apparatus.  ZOTltal.     The  screen  therefore  is 

perfectly  dark,  the  darkness  continuing  when  a  plate  of 
any  simply  refracting  substance,  as  for  example  glass 


INTERFERENCE  OWING  TO  DOUBLE  KEFRACTION.   817 

or  rock  salt,  is  introduced  between  the  two  Nicols.  If, 
on  the  other  hand,  a  lamina  of  a  doubly  refracting  cry- 
stal, as  for  example  a  natural  rhombohedron  obtained 
by  cleavage  of  Iceland  spar,  be  placed  at  C,  the  screen 
appears  alternately  dark  and  light  as  the  lamina  is  ro- 
tated around  the  axis  of  the  rays. 

This  behaviour  admits  of  an  easy  explanation.  If  a 
vertical  line,  M  N  (fig.  1  74),  be  conceived  to  be  drawn 
upon  the  screen,  the  position  of  the  principal  cleavage 
plane  of  the  first  Nicol's  prism, 
which  serves  as  a  polariser,  is  ob- 
tained ;  and  in  the  same  way  the  [f 
horizontal  line,  P  Q,  represents 
the  principal  cleavage  plane  of  the 
second  Nicol,  which  plays  the  part 
of  a  polariscope.  The  plate  of  spar 
is  now  introduced  between  the  po-  ^ 
lariser  and  the  polariscope,  in  the  ™ 

n       .    •  .  ,  . ,  Decomposition  of  vibrations. 

nrst  instance  in  such  a  way  that  its 

principal  cleavage  plane  coincides  with  the  direction  of 
the  vibration,  P  Q,  of  the  second  Nicol.  The  rays 
emerging  from  the  first  Nicol,  which  vibrate  parallel  to 
MN,  undergo  only  ordinary  refraction  in  the  crystal- 
line plate.  They  traverse  it  without  changing  the  di- 
rection of  their  vibration,  and  are  extinguished  by  the 
second  Nicol.  In  the  same  way  extinction  must  also 
occur  when  the  principal  cleavage  plane  of  the  plate 
coincides  with  the  plane  of  vibration,  MN,  of  the  first 
Nicol,  for  in  that  case  all  the  rays  pass  as  extraordina- 
rily refracted  rays  through  the  crystal,  whilst  they  pre- 
serve the  original  direction  of  vibration,  M  N.  If  the 
principal  plane  of  the  crystalline  plate  be  brought  into 
the  position  R  8,  it  only  allows,  in  accordance  with  the 


318  OPTICS. 

laws  of  double  refraction,  those  vibrations  to  traverse 
it  which  run  in  R  8,  or  at  right  angles  to  it,  UV. 
The  undulation,  MN9  as  it  emerges  from  the  first 
Nicol,  can  now,  since  it  forms  an  acute  angle  with  the 
principal  plane,  R  S,  neither  be  continued  completely  in 
the  ordinary  nor  in  the  extraordinary  ray ;  on  the 
contrary,  it  breaks  up,  in  accordance  with  the  laws  of 
motion,  into  two  undulations,  of  which  one,  running  in 
R  8,  traverses  the  crystal  as  an  extraordinary  ray, 
whilst  the  other,  vibrating  at  right  angles  to  the 
principal  plane  (in  U"F),  becomes  an  ordinarily  re- 
fracted ray. 

Two  rays  thus  reach  the  second  Nicol,  of  which  one 
vibrates  in  RS,  the  other  in  UV.  As  the  Nicol  only 
transmits  undulations  which  occur  in  its  principal  plane, 
P  Q,  each  of  these  two  rays  is  again  divided  into  two 
parts,  of  which  one  vibrates  in  P  Q,  the  other  in  M  N. 
The  two  sub-rays  whose  undulations  are  at  right  angles 
to  PQ  are  not  transmitted  by  the  Nicol ;  the  two  other 
sub-rays,  however,  whLh  take  place  in  its  chief  plane, 
P  Q,  penetrate  it,  and  illuminate  the  screen. 

We  thus  see  that  a  doubly  refracting  plate,  placed 
between  two  Nicols  at  right  angles  to  each  other,  causes 
the  field  of  vision  or  the  screen  to  be  dark  in  two 
positions,  when  its  principal  plane  coincides  with  that 
of  either  of  the  two  Nicols.  In  every  other  position 
light  passes  through  it,  and  the  screen  is  illuminated."* 
This  behaviour  is  a  positive  proof  of  its  doubly  refract- 
ing nature. 

142.  Of  the  two  sub-rays  which,  vibrating  in 
the  same  plane,  P  Q,  leave  the  second  Nicol,  the  first 

*  Except  only  when  the  plnte  is  cut  at  right  angles  to  its  optic  axis. 


INTEKFERENCE  OWING   TO   DOUBLE  KEFKACTION.        319 

originates  the  ordinary,  the  other  the  extraordinary 
ray,  of  which  each  propagates  itself  with  its  own  velo- 
city through  the  crystal  plate.  The  one  consequently 
lags  behind  the  other  to  the  extent  proportional  to 
the  thickness  of  the  lamina.  In  consequence  of  this 
difference  of  path  induced  by  double  refraction,  the  two 
rays  polarised  in  a  common  plane  of  vibration  occasion 
interference,  which  betrays  itself  when  the  difference  of 
path  is  not  too  great,  by  beautiful  colour  phenomena. 

The  plate  of  Iceland  spar  used  in  the  above  experi- 
ment is  too  thick  to  show  the  effects  of  interference. 
If  it  be  intended  for  this  purpose,  it  must  be  rendered  thin- 
ner by  grinding.  Crystallised  gypsum,  a  biaxial  doubly 
refracting  crystal  which  cleaves  easily  into  thin  laminae 
(Selenite)  is  a  convenient  substitute  for  the  Iceland 
spar  in  these  experiments  on  the  phenomena  of  inter- 
ference. If  such  a  plate  of  Selenite  be  placed  between 
the  crossed  Nicols,  it  behaves  like  the  plate  of  Iceland 
spar  ;  in  two  positions  of  the  lamina,  in  a  direction  in 
which  what  we  shall  term  its  principal  plane  is  parallel 
or  at  right  angles  to  the  direction  of  vibration  (MN, 
fig.  174)  of  the  polariser,  the  screen  remains  dark,  but 
in  every  other  position  it  exhibits  colours,  which  are 
brightest  when  the  principal  plane  of  the  lamina  makes 
an  angle  of  45°  with  the  axis  of  vibration  of  the  fiist 
Nicol. 

The  lamina  which  is  now  in  this  position  between 
the  Nicols  exhibits  a  beautiful  red  colour,  originating  in 
the  interference  of  the  two  sub  rays  vibrating  in  PQ. 

If    the    second   Nicol   be    now   rotated   from    the 

crossed   position,  the    screen   indeed   continues  to   be 

illuminated,  but  the  coloration   diminishes  in  bright- 

n^ss,    and    is    ultimately    replaced    by    perfect    white 

22 


820  OPTICS. 

light,  when  the  axis  of  vibration  of  the  Nicols  forma 
an  angle  of  45°  with  each  other.  If  it  be  turned  still 
further,  a  greenish  colour  appears,  which  finally,  when 
the  principal  planes  of  the  Nicols  are  parallel,  become? 
of  a  bright  green.  This  colour  is  the  result  of  the  inter- 
action of  the  two  part-rajs  vibrating  to  MN.  These 
colours — red  and  green — which  the  plate  of  Seleiiite 
exhibits  when  the  two  Nicols  are  parallel  to  or  at  right 
angles  with  one  another,  when  combined,  produce  white. 
This  can  be  immediately  demonstrated  by  replacing  the 
second  Nicol  with  an  ordinary  crystal  of  Iceland  spar 
(fig.  162,  B),  the  principal  plane  of  which  is  parallel  to 
that  of  the  first  Nicol.  It  is  traversed  by  both  pairs  of 
rays — those  vibrating  in  P  Q  as  well  as  those  in  M  N — 
in  consequence  of  which  the  former  undergoes  ordinary, 
the  latter  extraordinary  refraction;  two  coloured  images, 
the  red  and  the  green,  are  therefore  now  seen  at  the 
same  time  upon  the  screen,  so  placed,  however,  that  they 
partially  overlap.  The  part  common  to  the  two  images 
when  these  colours  are  blended  is  pure  white. 

1 43.  That  the  colours  must  be  most  lively  when  the 
principal  plane  of  the  lamina  of  Selenite  forms  an  angle 
of  45°  with  the  axis  of  the  vibration  of  the  polariser  is 
easily  demonstrated,  for  the  two  co-operating  divisional 
rays  are  then  equal  in  the  intensity  of  their  light,  and 
the  interference  which  gives  rise  to  the  colours  is  as 
complete  as  possible. 

The  reason  that  the  colours  observed  in  the  crossed 
and  parallel  position  of  the  Nicol  are  complementary 
to  each  other,  is  as  follows.  Let  us  suppose  that  a 
ray  proceeding  from  the  first  Nicol  strikes  the 
anterior  surface  of  the  lamina  in  the  point  0  (fig. 
I7i),  and  communicates  at  a  certain  given  moment 


INTERFERENCE   OWING  TO   DOUBLE    REFRACTION.     321 

to  the  particles  of  aether  at  0  a  motion  in  the  direction 
J  M,  that  is  to  say,  upwards.  Owing  to  the  double  re- 
fraction of  the  plate  of  Selenite  placed  at  an  angle  of 
45°,  this  motion  is  decomposed  into  two — of  which  the 
one  is  directed  to  the  right  and  upwards  (OR),  the 
othtr  to  the  left  and  upwards  (0(7).  The  former  is 
decomposed  into  a  motion  upwards  (OM"),  and  into 
another  to  the  right  (0  P)  ;  the  second  splits  into  a 
motion  upwards  and  into  one  to  the  left  (OQ).  The  two 
vertical  part-motions  thus,  so  far  as  only  the  action  of 
tLe  second  Nicol  comes  into  consideration,  coincide  in 
direction  ;  i/he  two  horizontal  ones  are  in  direct  opposi- 
tion, or,  in  other  words,  the  latter  alone  attain,  owing 
to  the  decomposition  effected  by  the  polariscope,  to  a 
difference  of  path  of  a  half  wave-length,  which  is  super- 
added  to  the  difference  of  path  already  effected  within 
the  plate  of  Selenite.  Were  the  Selenite  plate  just  so 
thick  that  one  ray  lagged  behind  the  other  three  half 
wave-lengths  of  the  red  (Fraunhofer's  line,  B),  this 
colour  must  vanish  when  the  Nicols  are  parallel;  whilst 
the  green  (6),  for  the  production  of  which  a  retardation 
of  two  whole  wave-lengths  occurs,  attains  its  greatest 
brilliancy.  The  lamina  therefore  exhibits  a  green 
mixed  colour  when  the  Nicols  are  parallel.  If  the 
Nicols  decussate,  a  half  wave-length  must  be  added  to 
the  difference  of  path  of  each  kind  of  ray.  The  re- 
tardation of  the  red  rays  then  amounts  to  two  whole, 
that  of  the  green  to  five  half  wave-lengths ;  and  whilst 
the  green  rays  extinguish  each  other,  the  red  attain 
their  highest  brilliancy.  The  lamina  therefore  now 
appears  of  a  red  tint,  which  is  exactly  complementary 
to  the  green. 

144.  We  can  also  obtain  direct  information  respect- 


822  OPTICS. 

ing  the  composition  of  the  tint  exhibited  by  a  crystalline 
plate  by  effecting  its  decomposition  with  a  prism.  If, 
whilst  the  Selenite  plate  just  described  is  introduced 
between  the  parallel  Nicols,  a  prism  be  placed  behind 
the  second  Nicol,  a  perfectly  dark  line  appears  in  the 
red  in  the  spectrum  which  is  thrown  upon  the  screen, 
proving  that  this  colour  is  deficient  in  the  green  light 
which  leaves  the  polariscope.  If  the  second  Nicol  be 
now  rotated,  this  stria,  without  altering  its  position, 
becomes  progressively  fainter,  and  ultimately,  when  the 
principal  planes  of  the  Nicols  are  inclined  to  each  other 
at  an  angle  of  45°,  vanishes ;  for  now,  since  only  one 
of  the  two  rays  (RS  or  UV,  fig.  174)  penetrates  the 
second  Nicol,  scarcely  any  interference  takes  place,  and 
the  white  light,  remaining  undiminished  in  intensity, 
betrays  itself  by  a  spectrum  without  any  spaces.  As  the 
Nicol  is  rotated  still  further,  a  slight  shade  makes  its 
appearance  in  the  green,  which,  as  the  Nicols  approach 
to  a  position  at  right  angles  with  one  another,  deepens 
into  complete  blackness. 

The  difference  of  path,  and  consequently  also  the 
tint  of  colour,  dependent  at  any  moment  upon  the  pris- 
matic decomposition,  varies  with  the  thickness  of  the 
plate.  The  thicker  the  Selenite  plate  is  the  greater  is 
the  number  of  dark  striae  (fig.  153)  that  appear  in  the 
spectrum,  and  so  much  the  nearer  does  its  interference 
col)ur  approximate  to  white,  for  reasons  that  hnve 
already  been  mentioned  in  speaking  of  the  colours  of 
thin  plates.  For  a  plate  of  Selenite  consequently  to 
exhibit  lively  colours,  its  thickness  must  not  exceed  0-3 
of  a  millimeter  (^nd  of  an  inch). 

In  order  to  exhibit  at  one  and  the  same  moment  all 
the  tints  of  colour  that  a  plate  of  Selenite  of  every  con- 


INTERFERENCE   OWING   TO   DOUBLE  REFRACTION.      323 

eeivable  thickness  may  show,  a  wedge-shaped  polished 
plate  may  be  employed.  By  means  of  a  polarising-  appa- 
ratus, with  the  arrangement  of  which  (fig.  1 75)  the  reader 
is  already  familiar,  the  image  produced  by  such  a  Sele- 
nite  wedge  may  be  thrown  upon  the  screen  ;  the  colony 
arranged  in  regular  order  parallel  to  the  edge  of  the 
prism,  exhibit  the  same  serial  sticcession  as  in  the  New- 
tonian rings  of  colour,  and  are  therefore  divided  in  the 
same  manner  into  orders,  and  named  in  the  same  way 
(gee  §  118).  The  introduction  of  a  concave  and  polished 
plate  of  Selenite  resembling  a  concave  lens  into  the 
polarising  apparatus  will  even  cause  the  colours  to  be 
arranged  in  concentric  rings.  It  may  be  seen,  in  fact, 
that  when  the  planes  of  vibration  of  the  polarising 
apparatus  are  at  right  angles  to  one  another,  a  system 
of  coloured  rings  with  dark  central  point  makes  its 
appearance,  which  differs  from  the  Newtonian  (fig.  151) 
rings  only  in  the  greater  brilliancy  of  the  colours. 

It  is  unnecessary  to  mention  that  all  the  phe- 
nomena considered  to  be  here  represented  to  an  audi- 
ence upon  a  screen  may  also  be  observed  by  an  individual 
if  a  Norreniberg's  polarising  apparatus  be  employed. 
When  used  for  this  purpose,  a  glass  plate  of  about  half 
its  height  is  introduced  into  the  apparatus  (fig.  163,  K', 
and  169,  m),  on  which  the  crystal  lamina  to  be  examined 
is  placed. 

145.  If  two  plates  of  Selenite  of  exactly  the  same 
thickness,  and  each  of  which  by  itself  produces  exactly 
the  same  tint,  be  now  superimposed  in  such  a  manner 
that  their  principal  planes  coincide  when  introduced  be- 
tween the  crossed  Nicols,  they  exhibit  another  colour 
(fig.  173),  namely,  that  which  corresponds  to  a  single 
plate  of  double  the  thickness  of  either  alone.  0  plac- 


824  OPTICS. 

ing  the  plates  on  one  another  in  such  a  manner  that  their 
principal  planes  decussate  at  right  angles,  the  screen  will 
remain  dark ;  nor  does  any  tint  of  colour  appear  when 
the  second  prism  is  rotated,  but  the  whole  behaves  just 
as  if  there  were  no  plate  of  Selenite  at  all,  for  that  ray, 
which  travels  more  slowly  in  the  first  lamina,  courses 
with  greater  rapidity  in  the  second,  its  speed  being  just 
as  much  accelerated  in  this  as  it  was  retarded  in  the 
first.  The  two  rays  which  leave  the  plate  have  therefore 
no  difference  of  path,  and  cannot  therefore  give  rise  to 
any  phenomena  of  interference  of  colour.  Two  unequally 
thick  plates,  crossed  in  the  same  way,  act  like  a  single 
plate  the  thickness  of  which  is  equal  to  the  difference 
of  thickness  of  the  two  plates,  since  the  one  only 
neutralises  in  part  the  action  of  the  other.  We  may 
hence  infer  that  interference  colours  may  be  produced 
by  the  decussation  of  two  thick  crystal  plates  neither 
of  which  appears  coloured  by  itself,  presupposing  that 
the  difference  of  their  thickness  is  not  too  great. 

This  character  may  also  be  made  use  of  in  order  to 
determine  the  gradation  of  the  colour  of  the  little  plate 
of  Selenite  in  the  serial  succession  of  the  interference 
colours,  with  the  aid  of  the  wedge-shaped  plate  of 
Selenite ;  for  if  the  plate  of  Selenite  be  placed  in  a  cross 
position  upon  the  wedge,  it  will  be  seen  that  the  striae 
are  altered  to  just  the  extent  that  the  plate  covers  the 
wedge.  Along  the  line  where  the  wedge  is  of  the  same 
thickness  as  the  plate,  this  last  abolishes  the  action  of 
the  wedge  ;  at  this  spot  therefore,  when  the  Nicols 
are  crossed,  there  must  be  a  completely  black  line.  The 
coloured  stria,  which  in  the  uncovered  part  of  the  wedge 
forms  the  prolongation  of  the  black  line,  now  presents 
just  that  colour  which  the  plate  exhibits  per  se ;  and  a 


INTERFERENCE   OWING  TO   DOUBLE'  REFRACTION.     325 

glance  is  sufficient  to  show  to  which  order  this  colour 
belongs. 

146.  In  the  above  experiments,  the  polarised  rays 
falling  upon  the  crystal  lamina  have  always  been 
parallel  to  one  another ;  in  a  plate  of  equal  thickness 
throughout  they  have  consequently  to  traverse  paths 
of  equal  length,  and  their  part- rays  possess  equal 
difference  of  path.  A  plate  of  equal  thickness 
throughout  exhibits,  therefore,  in  parallel  polarised 
light  a  single  and  uniform  tone  of  colour  in  its  whole 
extent. 

To  obtain  a  knowledge  of  the  behaviour  of  crystal- 
line plates  in  converging  polarised  light,  a  polarising 


Polarising  apparatus  of  Dubosq. 

apparatus,  constructed  by  Dubosq,  is  employed,  the 
essential  features  of  which  are  shown  in  fig.  1  75.  The 
parallel  rays  of  the  sun  falling  on  the  lens,  L,  are 
collected  into  a  cone  which  undergoes  double  refraction 
in  a  thick  crystal  of  Iceland  spar,  K,  which  serves  as  a 
polariser.  The  cone  of  the  ordinarily  refracted  rays, 
all  of  which  vibrate  at  right  angles  to  the  principal 
cleavage  plane  of  the  Iceland  spar,  passes  through  the 
hole  in  the  metal  plate,  S,  whilst  the  cone  of  extra- 
ordinarily refracted  rays  are  obstructed  by  the  metal 
plate.  The  crystal  plate,  the  action  of  which  upon  the 
converging  polarised  light  is  desired  to  be  investigated, 
is  placed  at  P,  near  the  apex  of  the  emerging  cone  of 


326  OPTICS. 

light ;  the  rays  diverging  from  the  crystal  plate,  P,  fall 
upon  a  second  lens,  which  projects  an  image  of  the 
interference  phenomena  produced  by  the  lamina  upon  a 
distant  screen.  Before  the  rays  reach  the  screen,  how- 
ever, they  are  made  to  pass  through  the  Nicol's  prism, 
N9  which  serves  as  a  polariscope. 

147.  The  phenomena  presented  by  plates  of  uniaxial 
crystals  cut  at  right  angles  to  the  optic  axis  in  converg- 
ingly  polarised  light  is  particularly  worthy  of  note.  That 
ray  of  the  cone  of  light  which  strikes  the  plate  vertically 
traverses  it  in  the  direction  of  the  axis,  and  undergoes 
no  double  refraction ;  every  other  ray,  however,  under- 
goes double  refraction,  which  is  greater,  because  the  path 
it  has  to  trarerse  within  the  crystal  is  longer,  in  propor- 
tion as  it  strikes  the  crystal  more  and  more  obliquely. 
Thus  it  comes  to  pass  that  the  differences  of  path  are 
always  greater  the  further  the  rays  are  distant  from  the 
axis  of  the  cone  of  light;  and  since  around  and  at  an 
equal  distance  from  the  optic  axis  the  two  circumstances 
which  determine  the  difference  of  path — the  degree  or 
amount  of  double  refraction  and  the  length  of  path  — 
are  equal,  it  follows  that  the  same  difference  of  path 
must  exist  for  all  points  of  a  circle  which  may  be  con- 
ceived as  drawn  upon  the  screen  around  the  point 
struck  by  the  axial  ray.  A  system  of  concentric  rays 
consequently  appears  upon  the  screen,  which  exhibit  a 
succession  of  colours  similar  to  those  in  the  rings  of 
Newton. 

When  the  planes  of  vibration  of  the  polarising  appa- 
ratus are  crossed,  the  system  of  rings  appears  to  be 
traversed  by  a  black  cross  (fig.  176,  A),  the  formation  of 
which  is  easily  explained  ;  for  since  the  optic  axis  is  per- 
pendicular to  the  surface  of  the  crystal,  every  straight 


INTERFERENCE   OWING   TO   DOUBLE   REFRACTION.     327 

line,  MN,  P  Q,  R8,  f7F(fig.  174)  drawn  through  the 
middle  point  of  the  system  of  rings  upon  the  screen, 
corresponds  to  a  principal  plane.  All  rays  that,  proceed- 
ing from  the  polariser,  strike  upon  the  cry stal-p. lite, 
vibrate  parallel  to  MN,  and  consequently  perpendicu- 
larly to  P  Q ;  they  proceed  therefore,  without  expe- 
riencing any  decomposition,  and  with  unaltered  direction 
of  vibration,  both  through  the  principal  plane,  M  N,  and 
through  the  principal  plane,  P  Q — through  the  former 
by  virtue  of  the  extraordinary,  and  through  the  latter 
by  virtue  of  the  ordinary  refraction — and  are  conse- 
quently not  transmitted  by  the  polariscope,  the  plane 
of  vibration  of  which  is  placed  at  P  Q.  A  black  cross 
thus  originates,  the  arms  of  which  are  parallel  with  the 
planes  of  the  polarising  apparatus.  In  every  other  prin- 
cipal plane,  R  8,  making  an  angle  with  the  plane  of 
vibration,  MN9  of  the  polariser,  a  decomposition  takes 
place  into  a  ray  vibrating  in  R  8,  and  one  perpendicular 
to  this,  the  part-rays  of  which  vibrating  in  P  Q,  in  con- 
sequence of  the  prolonged  difference  of  path,  interfere, 
and  thus  give  rise  to  the  system  of  rings.  % 

If  the  direction  of  vibration  of  the  polariscope  be 
parallel  to  that  of  the  polariser,  the  rings  that  appear 
are  complementary  to  the  foregoing ;  and  instead  of  the 
black  cross,  a  white  one  (fig.  1 76,  B)  is  obtained.  After 
what  has  been  already  said,  it  is  unnecessary  to  enter 
into  any  explanation  of  this  phenomenon. 

148.  A  plate  of  a  biaxial  crystal,  the  surfaces  of 
which  are  perpendicular  to  the  line  which  bisects  the 
acute  angle  of  the  two  optic  axes — as  for  example 
a  plate  of  Potassium  nitrate — exhibits  in  the  polarising 
apparatus,  when  the  planes  of  vibration  decussate,  the 
beautiful  phenomenon  depicted  in  fig.  177.  Two  sys- 


328 


OPTICS. 


terns  of  rings  are  then  seen,  each  of  which  surrounds  an 
optic  axis.  The  rings  of  higher  order,  approximating 
each  other  on  the  two  sides,  ultimately  blend  to  form 


176. 


Rings  of  colour  produced  by  uniaxial  crystals. 

peculiarly  shaped  curves,  which,  gently  undulating, 
surround  the  two  axial  points.  When  the  principal 
plane  passing  through  the  optic  axes  of  the  crystal 
plate  coincides  with  one  of  the  two  planes  of  vibration 


FIG.  177. 


Rings  of  colour  produced  by  biaxial  crystals. 

of  the  polarising  apparatus,  the  double  system  of  rings 
appears  cut  in  two  by  a  black  cross  (fig,  177,  A)  ;  but  if 
the  crystal  be  rotated,  the  cross  breaks  up  into  two  dark 


INTERFERENCE   OWING  TO    DOUBLE   REFRACTION.     320 

curved  brushes,  which,  when  the  above-named  principal 
plane  forms  an  angle  with  the  axis  of  polarisation  of 
45°,  presents  the  appearance  shown  in  fig.  177,  B.  If 
the  polariser  be  rotated  from  the  crossed  into  the 
parallel  position,  the  rings  present  complementary 
colours  to  the  foregoing,  and  the  black  brushes  change 
to  white  ones.  All  these  phenomena  are  explicable 
upon  the  laws  of  double  refraction  in  biaxial  crystals, 
and  upon  the  same  fundamental  propositions  on  which 
the  explanation  of  the  coloured  rings  of  uniaxial  crystals 
rests. 

The  peculiar  forms  of  the  systems  of  rings  affords  a 
means  of  distinguishing  biaxial  from  uniaxial  crystals, 
by  simple  examination  in  a  polarising  apparatus.  For 
the  subjective  observation  of  this  phenomenon,  the  polar- 
ising apparatus  of  Norremberg  may  be  employed,  a 
lens  being  added  both  above  and  below  the  glass  plate 
(K'9  fig.  168)  on  which  the  crystal  plate  is  placed. 

The  Tourmaline  forceps  or  tongs  (fig.  170)  are  still 
better  adapted  for  this  purpose,  rendering  the  addition 
of  the  lenses  unnecessary,  since,  when  placed  imme- 
diately in  front  of  the  eye,  they  permit  the  entry  of  rays 
into  it  coming  from  every  direction. 

149.  It  may  be  vshown,  with  the  aid  of  interference 
phenomena  in  polarised  light,  that  singly  refracting 
bodies  like  glass  may  also  under  certain  circumstances 
become  doubly  refracting ;  that  is  to  say,  acquire  the 
property  of  breaking  up  every  incident  ray  of  natural 
light  into  two  polarised  rays.  If  a  square  plate  of  glass 
fitted  into  a  kind  of  vice  be  placed  at  the  point  f 
(fig.  175)  of  Dubosq's  polarising  apparatus,  and  pressure 
be  exerted  upon  it  from  above  downwards  by  means  of 
the  screw,  it  is  indeed  compressed  in  this  direction,  but 


330  OPTICS. 

extended  in  the  hoiizontal  one.     The  arrangement  of 

O 

its  molecules  is  now  no  longer  as  before  the  same  in  all 
directions,  and  the  plate  becomes  doubly  refracting  in 
consequence  of  the  altered  position  of  its  molecules  ; 
and  thus  the  screen,  which  previously  to  the  pressure 
being  exercised  was  dark  on  account  of  the  crossed 
position  of  the  planes  of  vibration,  now  presents  a  bright 
image  of  the  plate,  traversed  by  a  dark  cross.  The 
property  of  double  refraction  may  be  permanently  con- 
ferred upon  a  piece  of  glass  by  powerfully  heating  and 
then  suddenly  cooling  it.  If  a  disc  of  glass  which  has 
been  thus  treated  be  placed  in  the  apparatus,  a  beautiful 
system  of  coloured  rings  with  a  black  cross  comes  into 
view,  just  as  in  the  case  of  a  piece  of  Iceland  spar  cut 
at  right  angles  to  its  optic  axis.  A  black  cross  also 
appears  in  the  case  of  a  square  glass  plate,  and  in  each 
of  the  four  angles  is  a  beautiful  system  of  rings  that 
may  be  compared  with  the  eye  of  a  peacock  (fig.  178). 

These   phenomena   furnish    additional   evidence   of 
the  intimate  connection  between  the  doubly  refracting 
powers  of  different  substances,  and  the 
arrangement  of  their  molecules,  to  which 
reference  has  already  been  made  in  the 
chapter  devoted  to  the  double  refrac- 
tion of  crystals.     The  double  refraction 
of    compressed    and     suddenly    cooled 
^ass    *s    nevertheless    essentially    dif- 
piateo{ygiass.°led    ferent  from  that  of  crystals.     In  order 
to   project  the   system  of  rings  of  the 
g:lass  disc  UDon   the   screen,  it  must  be  placed  at  the 
point  P  -;  *  the  rays  by  which   it  is  struck  are  nearly 

*  The  little  plate  of  gypsum,  the  Selenite  wedge,  and  such  bodies  gene- 
rally as  are  used  in  the  experiments  mentioned  above,  and  the  behaviour 


INTERFERHNCE   OWING  TO   DOUBLE   REFRACTION.     & 

parallel,  and  traverse  the  plate  in  the  same  direction  and 
with  the  same  length  of  path.  The  difference  of  path 
which  gires  rise  to  the  system  of  rings  can  therefore 
only  be  due  to  the  fact  that  the  double  refraction,  whilst 
the  course  of  the  rays  remains  unaltered,  increases  towards 
the  periphery  of  the  plate.  In  a  crystal,  on  the  contrary, 
the  double  refraction  is  at  all  points  the  same  for  the 
same  direction  of  the  rays. 

of  which  in  polarised  light  is  desired  to  be  investigated,  must  bo  placed 
at  th-'  same  point. 


332  OFncs. 


CHAPTER   XXY. 

CIRCULAR    POLARISATION. 

150.  IF  a  plate  of  Iceland  spar  cut  at  rig-lit  angles 
to  the  optic  axis  be  placed  between  two  Nicol's  prisms 
FlG  179  (fig.  179),  the  parallel  polarised 

rays  emerging  from  the  first 
Nicol  run  collectively  through 
the  plate  in  the  direction  of  the 
optic  axis,  without  undergoing 
double  refraction  or  any  altera- 
,  ,  tion  in  the  direction  of  their 

vibration.  On  rotating  the  second 

Two  Nicol's  prisms.  & 

Nicol,  those  variations  of  light 

and  shade  are  only  seen  which  would  otherwise  occur 
in  the  absence  of  the  crystal  plate. 

All  uniaxial  crystals,  with  the  exception  of  Quartz, 
behave  in  the  same  way.  If  a  polished  Quartz  plate,  cut 
at  right  angles  to  the  optic  axis,  be  inserted  between 
the  two  Nicols,  the  screen  appears  of  a  lively  colour,  the 
colour  varying  with  the  position  of  the  Nicol,  but  never 
being  dark.  The  colours,  gradually  passing  into  one 
another  through  all  intermediate  tints  as  the  polar iscope 
is  turned,  which  are  seen  upon  the  screen,  are  suc- 
cessively red,  orange,  yellow,  green,  blue,  violet ;  and 
these  are  repeated  in  the  same  order  as  the  rotation  is 
continued. 


CIRCULAR  POLARISATION.          .  333 

These  colours  are,  however,  by  no  means  pure 
spectrum  colours,  and  their  composition,  like  the  colours 
of  Selenite,  can  be  determined  by  prismatic  decomposi- 
tion. Thus,  if  the  green  light  which  is  emerging  from 
the  polariscope  in  its  present  position  be  allowed  to 
pass  through  a  prism,  a  spectrum  is  produced  the  red 
part  of  which  exhibits  a  perfectly  black  stria,  whilst  the 
orange  and  red  are  feebly,  and  the  green  and  blue  more 
vividly  luminous.  If  the  polariscope  be  turned  in  the 
same  direction  as  before,  the  black  line  is  seen  to  travel 
gradually  towards  the  more  refrangible  end  of  the  spec- 
trum, and  to  blot  out  in  succession  the  orange,  yellow, 
green,  blue,  and  violet  colours,  finally  being  lost  in  the 
extreme  violet,  in  order  to  reappear  at  the  red  end  of 
the  spectrum.  It  is  thus  rendered  evident  that  the  tints 
which  were  seen  when  the  prism  was  not  used  upon  the 
screen  are  mixtures  of  all  the  simple  colours  left  after 
the  extinction  of  the  one  covered  by  the  dark  stria. 

The  position  of  the  second  Nicol,  which  corresponds 
to  a  definite  position  of  the  dark  stria,  is  capable  of 
being  read  off  if  the  frame  be  provided  with  a  marker, 
z,  pointing  to  a  divided  circle,  K,  on  the  axis  of  which 
the  tube  rotates. 

The  Nicol  can  only  extinguish  those  rays  that  vibrate 
at  right  angles  to  its  principal  plane.  Before  the  Quartz 
plate  was  inserted,  all  vibrations  were  parallel  to  the 
vertically  placed  principal  plane  of  the  first  Nicol  (in 
the  direction  of  the  arrow,  fig.  180) ;  and  they  were 
therefore  collectively  extinguished  and  the  screen  was 
perfectly  dark,  since  the  principal  plane  of  the  second 
Nicol  was  horizontal,  and  thus  decussated  at  right 
angles  with  that  of  the  first.  But  after  the  Quartz  plate 
is  inserted  (the  thickness  of  which  is  3-75  of  a  milli- 


384 


OPTICS. 


FIG.  180. 


meter),  the  second  Nicol  must  be  rotated  60°  from  the 
crossed  position,  by  which  means  the  red  rays  undergo 
extinction  in  consequence  of  the 
dark  stria  in  the  red  part  of  the 
spectrum.  The  direction  of  vi- 
bration of  the  red  rays  is  con- 
sequently at  right  angles  to  the 
present  position  of  the  principal 
plane,  and  thus,  through  the  ac- 
tion of  the  Quartz,  it  has  been 
rotated  about  (50°  from  the  vertical 
position  which  it  previously  had  in 
common  with  all  the  other  kinds 
of  rays,  and  comes  to  occupy 
the  position  r  r'  (fig.  180,  upper 
figure).  Similarly,  the  plane  cf 
vibration  of  the  yellow  rays  has 
undergone  a  rotation  of  90°  (ggf), 
and  that  of  the  violet  a  rotation 
of  165°  (vv'}.  In  the  adjoining 
figure  the  direction  of  the  vibrations  which  are  pursued 
by  the  chief  colours  of  the  spectrum,  after  their  passage 
through  the  Quartz  plate,  is  indicated  in  a  very  easily 
intelligible  manner. 

The  action  of  the  Quartz  plate  thus  consists  in  effecting 
a  rotation  of  the  plane  of  vibration  of  the  polarised  rays, 
the  amount  of  rotation  varying  for  each  kind  of  homo- 
geneous light,  and  being  greater  in  proportion  to  the 
number  of  vibrations.  In  consequence  of  this  dispersion 
of  the  colours  in  various  directions  of  vibration,  white 
light  becomes  broken  up  in  a  mode  which  is  comparable 
with  the  dispersion  of  colour  by  ordinary  refraction,  \ 
and  on  this  account  has  received  the  name  of  circular 
or  rotatory  dispersion. 


Rotation  of  the  planes  of 
vibration  in  Quartz. 


CIRCULAR  POLARISATION,  385 

The  angle  of  rotation  above  given  refers  to  a  Quartz 
plate  of  3-75  millimeters  thick.  When  plates  of  various 
thickness  are  employed,  it  is  found  that  for  any  given 
homogeneous  colour  the  rotation  increases  in  propor- 
tion to  the  thickness  of  the  plate.  If  therefore  the 
amount  of  rotation  is  known  for  any  particular  thick- 
ness, it  may  be  immediately  calculated  for  any  other 
thickness.  Broch  measured  the  angle  of  rotation  at 
which  the  dark  stria  in  the  spectrum  occupied  in  suc- 
cession the  position  of  the  principal  Fraunhofer's  lines, 
and  found  the  following  values  for  a  Quartz  plate  of  one 
millimeter  in  thickness : — 

B  C  D  E  F  G 

15°  30     17°  24     21°  67     27°  46     32°  50     42°  20. 

151.  In  the  case  of  the  Quartz  plate  used  in  the 
foregoing  experiments,  whilst  the  dark  line  moves  along 
the  spectrum  from  the  red  to  the  violet  end,  the  polari- 
scope  must  be  so  rotated  that  the  indicator,  z9  moves 
over  the  divided  circle,  K,  in  the  direction  of  the  hands 
of  a  watch,  that  is,  to  the  right.  But  there  are  other 
specimens  of  Quartz  in  which  the  polariscope  must 
be  rotated  in  the  opposite  direction,  or  to  the  left, 
because  the  dark  line  moves  in  the  spectrum  from  the 
violet  to  the  red  end.  Quartz  crystals  are  consequently 
distinguished  as  rotating  to  the  right  or  to  the  left.  Both 
kinds,  with  equal  thickness  of  plate,  rotate  the  plane  of 
vibration  of  the  same  homogeneous  light  equally,  but  in 
opposite  directions.  The  lower  half  of  fig.  180  repre- 
sents the  rotation  of  the  various  colours  in  the  case  of 
a  plate  of  3' 75  millimeters  in  thickness  rotating  to  the 
left,  just  as  the  upper  half  shows  it  in  the  case  of  a 
plate  of  equal  thickness,  but  rotating  to  the  right. 
23 


33<3  OPTICS 

152..  In  order  to  pave  tlie  way  for  the  right  under- 
standing of  the  process  by  which  the  rotation  of  the 
plane   of    vibration    is  effected    in  a 

1*IG.  Jol« 

Quartz  crystal,  the  motion  must  be 
investigated  that  is  produced  by  the 
co-operation  of  two  vibrations  at 
right  angles  to  each  other;  and  for 
this  purpose  nothing  is  superior  to 
the  vibrations  of  an  ordinary  pen- 
dulum. A  heavy  leaden  weight 
(fig.  181),  pointed  below,  is  suspended 
by  a  wire  from  the  ceiling  over  a 
platter,  the  point  when  at  rest  being 
at  0.  Through  the  point  0  two  lines, 
A  B  and  C  D,  are  drawn  at  right 
angles  on  the  plane  of  the  table.  If 
the  pendulum  be  brought  to  Ay  and 
then  released,  or  if,  when  it  is  at 
rest,  a  blow  be  communicated  to  it  in  the  direction  OA, 
it  swings  to  and  fro  in  the  line  0  A.  In  the  same  way 
it  vibrates  along  the  line  CD  if  it  be  struck  in  this 
direction,  or  be  brought  to  C  or  D  and  then  released. 
The  period  of  vibration,  that  is  to  say,  the  time  requisite 
for  its  passage  to  and  fro,  is  the  same  in  whichever 
direction  the  vibrations  are  made  to  take  place. 

The  question  now  arises,  however,  what  movement 
will  the  pendulum  perform  if  it  be  simultaneously  acted 
upon  by  two  impulses  acting  at  right  angles  to  each 
other  ?  Let  the  pendulum  be  made  to  vibrate  in  the 
direction  AB,  and  when  it  has  reached  the  extreme 
point  .of  its  motion  at  A,  let  a  blow  be  given  to  it  in  the 
direction  A  a.  at  right  angles  to  A  B,  the  strength  of 
which  is  just  sufficient,  if  the  pendulum  be  moving  in 


CIRCULAR  POLARISATION.  387 

this  direction  alone,  to  send  it  as  far  to  the  side  from 
its  present  position  as  it  was  in  the  first  instance  moved 
at  the  moment  of  the  blow  from  the  position  of  rest  at 
0.  The  result  observed  is  that  the  lead  weight  de- 
scribes with  uniform  velocity  a  circle,  ACBDA,  in  the 
direction  indicated  by  the  arrows. 

Had  the  vibration  of  the  pendulum  been  measured 
from  the  moment  in  which  it  shortly  before  went  in  the 
direction  BA  through  the  point  of  rest,  it  would  be  found 
to  have  already  performed  a  quarter- vibration*  when  it 
received  the  impulse  in  the  direction  A  a.  It  is  thus  seen 
that  two  movements  of  vibration  at  right  angles  to  each 
other,  of  which  each  is  rectilinear  in  itself,  combine  to  form 
a  circular  motion  when  one  is  a  quarter-vibration  before 
the  other.  In  the  case  illustrated  by  the  figure,  when  the 
vibration  directed  to  0  A  is  antecedent  to  that  directed 
to  0  0,  the  circular  movement  takes  place  in  the  direc- 
tion of  the  hands  of  a  watch,  or  to  the  right,  as  is  indi- 
cated by  the  arrows.  If  the  impulse  be  given  in  the 
opposite  direction,  a  circular  movement  to  the  left  is 
produced.  The  circular  movement  to  the  left  is  also 
engendered  if  the  pendulum  be  first  put  into  vibration 
in  the  direction  00;  and  when  it  has  arrived  at  0,  an 
impulse  in  the  direction  OA  be  given,  that  is,  if  the 
movement  in  the  direction  OA  is  a  quarter- vibration 
behind  that  in  0  C.  The  time  required  for  the  comple- 
tion of  an  entire  circle  is  always  equal  to  the  period  of 
vibration  proper  to  the  pendulum. 

If  the  impulse  given  at  A  be  more  powerful  than 
that  which  it  originally  received,  the  leaden  weight  is 

*  It  may  not  perhaps  be  superfluous  to  observe  that  ty  one  entire  vibra- 
tion is  meant  the  motion  OAOBU,  or  complete  to  and  fro  movement 
Flic  motion  0  A  is  consequently  a  quarter- vibration. 


338  OPTICS. 

propelled  to  a  grea.ter  distance  laterally  in  the  direction 
O  C,  and  the  pendulum  moves  in  an  ellipse  the  smaller 
axis  of  which  is  A  B ;  but  if  the  impulse  be  less  powerful, 
A  B  becomes  the  greater  axis  of  the  ellipse  described 
by  the  pendulum.  Impulses  applied  to  the  pendulum 
whilst  it  is  passing  from  0  to  A,  or  from  0  to  B,  like- 
wise occasion  elliptical  paths  of  vibration,  the  axes  of 
which  however  are  no  longer  in  the  lines  A  B  and  CD. 
If  the  lateral  impulse  in  the  direction  0  C  be  com- 
municated at  the  moment  when  the  pendulum  passes 
through  its  position  of  rest,  it  assumes  again  a  rectilinear 
movement,  directed  however  neither  towards  A  nor 
towards  0,  but  along  some  intermediate  line ;  in  this 
case  the  one  movement  precedes  the  other  either  not 
at  all  or  a  certain  number  of  half- vibrations. 

153.  The  conditions  of  movement  which  were  ob- 
served in  the  pendulum  may  also  be  followed  in  the 
case  of  light  with  the  aid  of  thin 
crystalline  laminse.  Mica,  which 
easily  splits  up  into  still  thinner 
plates  than  Selenite,  is  especially 
adapted  for  this  purpose.  If  a 
thin  plate  of  Mica  be  placed  be- 
tween the  two  Nicols  (fig.  179),  so 
that  its  principal  plane  R  8  (fig. 
*  182),  forms  an  angle  of  45°  with 

Decomposition  of  vibrations.     . ,  .          „      .,         .  .  n/r  -\-r       r?  j_ i 

the  axis  of  vibration,  If  A,  of  the 

polariser  (the  fig.  182  being  now  considered  as  applied 
to  the  surface  of  the  lamina  from  which  the  light 
emerges),  two  equally  luminous  rays  are  found  to  emerge 
from  the  plate,  of  which  one  vibrates  in  R  89  the  other 
at  right  angles  to  it  in  U  V.  The  particle  of  sether 
lying  at  0  on  the  plane  of  emergence  of  the  lamina  is 


CIRCULAR  POLARISATION.  339 

consequently,  like  the  pendulum  weight,  affected  con- 
temporaneously by  two  impulses  at  right  angles  to  each 
other,  and  assumes  a  circular,  elliptic,  or  rectilinear 
motion  according  to  the  amount  of  the  start  which  one 
vibration  has  over  the  other. 

The  Mica  plate  used  in  these  experiments  is  just  so 
thick  that  it  occasions  a  difference  of  path  of  a  quarter 
wave-length  of  yellow  light  between  the  two  rays 
vibrating  at  right  angles  to  each  other.  Under  these 
circumstances  it  is  obvious  that  for  this  colour  the 
vibration  of  the  more  quickly  propagated  ray  (which 
maybe  assumed  to  be  U  F),  on  arriving  at  the  par- 
ticle 0  precedes  by  a  quarter- vibration  that  of  the  moro 
slowly  propagated  ray  (R  S). 

The  particle  0  assumes  therefore  a  circular  move- 
ment to  the  right  the  period  of  revolution  of  which  is 
equal  to  the  duration  of  vibration  of  yellow  light,  and 
which  communicates  itself  to  the  successive  particles  of 
seiher  arranged  serially  in  the  direction  of  the  ray. 
Each  of  these  moves  in  a  circle,  since  its  revolution 
begins  somewhat  later  than  the  preceding,  the  plane  of 
which  is  perpendicular  to  the  ray  around  this ;  and  if 
the  coetaneous  position  of  the  aether  particles  at  any 
moment  be  conceived  to  be  connected  by  a  curved  line, 
a  wavy  line  will  be  obtained  which  would  wind  round 
the  ray  like  a  screw,  a  complete  turn  of  the  screw 
corresponding  to  each  wave-length. 

A  ray  of  light  of  this  quality  is  said  to  be  circularly 
polarised,  whilst  the  rays  that  have  hitherto  been  curtly 
termed  6  polarised '  will  henceforward  be  referred  to  as 
rectilinearly  polarised,  because  their  vibrations  take 
place  in  straight  lines  perpendicular  to  the  direction  of 
the  ray. 


840  OPTICS. 

The  difference  of  path  of  the  two  rays  vibrating  at 
right  angles  to  one  another  in  the  above- mentioned 
Mica  plate  amounts  to  an  exact  quarter-wave  for  the 
brightest  yellow  light  alone ;  it  is  somewhat  less  for  red 
rays  and  for  blue  somewhat  more.  The  plate  conse- 
quently communicates  to  the  yellow  rays  alone  a  per- 
fectly circular,  whilst  the  rest  have  a  more  or  less  elliptic 
polarisation.  Since,  however,  when  the  plate  is  thin  the 
deviations  from  the  circular  form  are  very  inconsider- 
able, the  white  light  that  is  transmitted  may  be  re- 
garded as  being  almost  completely  circularly  polarised. 

154.  The  white  fasciculus  of  rays  proceeding  from 
the  quarter- wave  Mica  plate  now  demands  examination. 
After  allowing  it  to  pass  through  the  second  Nicol, 
By  it  will  be  found  that  the  screen  remains  equally 
bright  in  whatever  direction  the  Nicol  may  be  rotated.  A 
circularly  polarised  ray  may  in  fact,  since  its  quality  is 
the  same  all  round,  exhibit  no  laterality ;  it  behaves 
itself  when  examined  with  a  Nicol  like  an  ordinary 
ray  of  light.  That  it  is  not  such  a  natural  ray  is 
immediately  rendered  apparent  if  a  second  Mica  plate 
of  equal  thickness,  but  with  its  principal  plane  at  right 
angles,  be  interposed.  The  original  rectilinear  polari- 
sation is  again  shown  to  be  present;  the  screen  ceases 
to  be  illuminated  when  the  plane  of  vibration  of  the 
second  ISTicol  decussates  with  that  of  the  first.  The 
very  case  mentioned  above  in  regard  to  the  pendulum  is 
before  us,  namely  that  neither  of  the  two  perpendicular 
vibrations  precedes  the  other,  so  that  the  two  equal 
vibrations,  0  R  and  0  U,  combine  to  produce  a  recti- 
linear vibration,  0  M,  the  axis  of  which  bisects  the 
angle,  R  0  U.  If  the  second  Mica  plate  be  superimposed 
upon  the  first,  with  its  principal  plane  parallel,  the  dif- 


CIRCULAR  POLARISATION.  341 

Terence  of  path  between  0  U  and  OR  amounts  to  a  half 
wave-length,  and  again  gives  rise  to  a  rectilinearly  po- 
larised ray  which  now  vibrates  in  P  Q,  and  consequently 
disappears  when  the  plane  of  vibration  of  the  second 
Nicol  is  parallel  to  that  of  the  first.  A  quarter- wave 
Mica  plate  may  thus  be  used  for  the  purpose  of  recog- 
nising circularly  polarised  from  rectilinearly  polarised 
and  from  natural  light,  as  it  is  capable  of  converting  a 
rectilinearly  polarised  into  a  circularly  polarised  ray  of 
light;  it  may  also,  conversely,  change  circularly  pola- 
rised light  into  rectilinearly  polarised,  whilst  it  allows 
a  natural  ray  of  light  to  continue  unaltered. 

155.  In  the  above-mentioned  experiment  with  a 
circularly  polarising  Mica  plate,  it  has  been  taken  for 
granted  that  the  more  rapidly  moving  ray  vibrates  in 
the  axis  0  U ;  on  this  supposition  the  circular  move- 
ment of  the  sether  particles  takes  place  to  the  right. 
If  the  Mica  plate  be  rotated  in  its  plane  90°,  so  that  the 
vibration  in  the  axis  0  R  is  accelerated  about  a  quarter- 
vibration,  the  plate  occasions  the  light  to  be  polarised 
circularly  to  the  left.  When  this  is  examined  with  the 
Nicol  and  with  the  second  Mica  plate,  it  behaves  in 
exactly  the  same  manner  as  that  polarised  to  the 
right,  and  cannot  be  distinguished  from  it  by  these 
means.  The  difference,  however,  can  be  instantly 
recognised  if  a  plate  of  Selenite,  with  its  principal  plane 
placed  at  45°,  be  interposed  between  the  Mica  plate,  (7, 
and  the  second  Nicol,  B  (fig.  179),  at  right  angles  with 
the  first,  the  phenomena  of  colour  of  which  in  recti- 
linearly polarised  light  are  now  sufficiently  known.  The 
light  upon  the  screen  now  appears  coloured,  the  colour 
varying  according  to  whether  the  Mica  plate  is  intro- 
duced in  right-  or  in  left-handed  circular  polarisation. 


342  OPTICS, 

If,  for  example,  the  colour  be  in  the  first  instance 
bluish  green,  the  complementary  rose-red  tint  appears 
in  the  second  instance.  In  that  case  the  principal 
planes  of  the  Selenite  and  of  the  Mica  plate  are  parallel 
to  each  other,  and  to  the  difference  of  path  which  the 
Selenite  occasions  must  be  added  that  difference,  amount- 
ing to  a  quarter  wave,  which  is  induced  by  the  Mica 
plate  ;  in  the  second  case,  where  the  principal  planes  of 
the  two  plates  decussate  at  right  angles  to  each  other, 
the  difference  of  path  occasioned  by  the  plate  of  Selenite 
is  diminished  by  a  quarter  wave.  The  difference  of  path 
in  light  polarised  circularly  to  the  right  exceeds  conse- 
quently by  a  half  wave  that  polarised  circularly  to  the 
left,  so  that  there  all  those  rays  are  extinguished,  which 
are  here  most  brilliant,  and  vice  versa.  The  mixed 
colours  therefore  which  occur  in  the  two  cases  must  be 
complementary  to  each  other. 

156.  Recurring  for  a  moment  to  the  pendulum 
(fig.  181),  and  conceiving  that  the  leaden  weight  whilst 
it  is  at  A  (fig.  183)  receives  an  im- 
pulse not  only  in  the  direction  A  a, 
but  coincidently  also  an  equally 
powerful  impulse  in  the  opposite 
direction,  A  of,  the  first  impulse, 
combined  with  the  impulse  which  the 
pendulum  already  possesses  in  the 
direction  of  the  line  A  5,  would  lead 
to  a  circular  movement  to  the  right; 

Combined    effect    of    two 

opposite  circular  vibra-   the  second,  to  a  similar  movement  to 


the  left.  If  the  two  impulses  acted 
simultaneously,  they  would  neutralise  each  other,  and 
the  pendulum  would  continue  to  vibrate  to  and  fro 
along  the  straight  line,  A  B,  as  if  nothing  had  happened. 


CIRCULAR   POLARISATION.  343 

But  supposing  the  second  impulse  to  occur  later,  after 
tlie  pendulum  had  in  consequence  of  the  first  impulse 
already  performed  the  circular  movement,  A  ry  and  sup- 
posing this  impulse  to  be  in  opposition  to  the  direction 
of  the  movement  it  possesses  at  the  point  r,  a  rectilinear 
movement  will  obviously  be  developed  along  rr'.  From 
this  it  results  that  a  vibrating  body  acted  on  coin- 
cidently  by  two  equal  but  opposite  circular  forces  will 
acquire  a  rectilinear  vibrating  movement,  which  takes 
place  along  that  diameter  of  the  circle  at  the  terminal 
point  of  which  it  received  the  impulses. 

If  this  proposition  be  applied  to  the  vibrations  of 
light,  it  follows  that  a  rectilinearly  polarised  ray  is 
always  the  result  of  the  combined  effect  of  two  rays  of 
light  polarised  circularly  in  opposite  directions,  of  equal 
brilliancy  and  equal  number  of  vibrations,  following  the 
same  path ;  and  conversely,  it  may  be  said  that  every 
rectilinearly  polarised  ray  may  be  regarded  as  composed  of 
two  equally  bright  rays  of  light  polarised  circularly  in 
opposite  directions. 

157.  This  representation  or  explanation  of  the  phe- 
nomena founded  on  the  general  laws  of  motion,  and  to 
the  eifect  that  a  rectilinearly  polarised  ray  of  light  con- 
sists of  two  rays  polarised  circularly  in  opposite  direc- 
tions, would  only  possess  a  theoretic  significance  were 
there  not  bodies  which  act  upon  light  polarised  circu- 
larly to  the  right  differently  to  light  polarised  circularly 
to  the  left.  Eresiiel  has  shown  that  Quartz  is  such  a 
body. 

The  fact  of  the  rotation  of  the  plane  of  vibration 
through  a  plate  of  Quartz  becomes  perfectly  intelligible 
if  it  be  admitted  that  rays  polarised  circularly  in  oppo- 
site directions  are  propagated  with  different  velocities 


344  OPTICS. 

along  the  axis  of  a  crystal  of  Quartz.  A  rectilinea,rly 
polarised  ray  of  light  must,  on  its  entrance  into  a 
Quartz  plate,  be  broken  up  into  two  rays  polarised  cir- 
cularly in  opposite  directions,  which,  after  they  have 
traversed  the  plate  with  unequal  velocity,  on  their  exit 
again  combine  to  form  a  rectilinearly  pobirisecVray,  TEe" 
plane  of  vibration  of  which  differs  either  to  the  right  or 
left  of  that  of  the  incident  ray  according  as  the  right  or 
left  circular  impulse  is  antecedent  and  affects  earlier 
the  particles  of  sether  in  contact  with  the  surface  of 
emergence.  The  greater  the  thickness  of  the  Quartz 
plate,  the  greater  is  the  retardation  of  one  of  the  two 
rays,  and  the  greater  must  be  the  rotation  of  the  plane 
of  vibration.  The  circumstance  that  equally  thick  plates 
of  Quartz  rotate  the  plane  of  vibration  to  the  right 
and  to  the  left  to  the  same  extent,  although  in  opposite 
directions,  indicates  that  the  rapidity  of  propagation  of 
the  rays  polarised  circularly  in  opposite  directions 
are  the  same  in  the  two  kinds  of  Quartz,  and  are  only 
interchangeable  so  far  that  tha.t  ray  which  has  a  greater 
velocity  in  the  one  crystal  moves  'more  slowly  in  the 
other. 

158.  If  the  two  kinds  of  circularly  polarised  rays 
are  propagated  with  different  velocities  parallel  to  the 
axis  of  the  Quartz,  a  peculiar  kind  of  double  refraction 

must  take  place  in  this  direc- 

rJG.  184.  i 

tion,  by  means  of  which  an 
incident  rectilinearly  polarised 
ray  is  decomposed  into  two  rays 
Double  p^n  If  Quartz.  polarised  circularly  in  opposite 
directions.  In  the  Quartz  plates 

that  have  hitherto  been    employed,   and    which   were 
struck   rectilinearly    by  the    incident  rays,    an    actual 


CIRCULAR  POLARISATION.  345 

decomposition  can  certainly  not  take  place,  because 
although  the  two  rays  are  propagated  with  different 
velocities,  they  course  in  the  same  direction.  Fresnel, 
by  an  ingenious  combination  of  two  prisms  of  Quartz 
rotating  in  opposite  directions,  did  however  effect  this 
decomposition,  and  thus  demonstrated  beyond  a  doubt 
the  correctness  of  the  explanation  previously  given  of 
the  rotation  of  the  plane  of  vibration. 

Fresnel's  double  prism  (fig.  184)  consists  of  two 
elongated  rectangular  prisms  of  Quartz  each  having  an 
acute  angle  A  C B  of  7°,  one  of  which  is  cut  from  a 
prism  rotating  to  the  right,  and  the  other  from  a  prism 
rotating  to  the  left.  Being  cemented  together  by  their 
oblique  surfaces,  A  C,  they  form  a  rectangular  column 
the  terminal  surfaces  of  which,  A  B  and  C  D,  are  per- 
pendicular to  the  optic  axis.  If  a  rectilinearly  pola- 
rised beam  be  allowed  to  fall  through  a  round  opening 
upon  the  surface  A  B,  it  undergoes  decomposition  into 
two  rays  polarised  circularly  in  opposite  directions 
which  traverse  the  first  prism  with  different  velocities, 
but  in  a  path  common  to  both.  The  ray  which  in  the 
first  prism  was  the  most  rapid,  on  entering  the  second 
prism  becomes  the  less  rapid  of  the  two,  and  there- 
fore approaches  to  the  perpendicular  (indicated  in  the 
figure  by  the  dotted  line)  ;  on  the  other  hand,  the  ray 
moving  more  slowly  in  the  first  prism  is  propagated 
more  rapidly  in  the  second,  and  must  consequently 
recede  from  the  perpendicular.  Two  separate  fasci- 
culi consequently  emerge  from  the  surface  CD,  which 
produce  two  round  spots  of  light  upon  the  screen, 
the  borders  of  which  overlap  to  some  extent.  When 
looked  at  through  a  Nicol  placed  between  C  I)  and  the 
screen,  the  two  beams  prove  to  be  circularly  polarised, 


346  OPTICS. 

and  if  a  plate  of  Selenite  be  placed  between  the  double 
prism  and  the  Nicol  at  an  angle  of  45°,  one  of  the 
spots  of  light  appears  of  a  bluish  green,  the  other  of  a 
rose-red  tint,  whilst  the  area  common  to  both  remains 
white.  The  occurrence  of  these  complementary  colours 
demonstrates  that  one  of  the  beams  is  circularly  pola- 
rised to  the  right,  the  other  to  the  left.  This  experi- 
ment therefore  furnishes  decisive  proof  that  a  recti- 
linearly  polarised  ray  of  light  is  decomposed  by  the 
Quartz  into  two  rays  moving  with  unequal  velocity  and 
polarised  circularly  in  opposite  directions. 

159.  The  power  of  circular  double  refraction  belongs 
to  only  a  few  substances  besides  quartz,  and  is  not 
associated  with  any  definite  crystalline  system ;  it  is 
exhibited  by  a  few  singly  refracting  crystals  belonging 
to  the  regular  system,  as  for  example  by  Sodium 
chloride  in  all  directions.  In  doubly  refracting  crystals, 
as  for  example  in  Quartz,  it  can  only  be  perceived  in 
directions  that  are  nearly  parallel  to  the  optic  axis, 
because  in  every  other  direction  they  are  concealed  by 
the  ordinary  double  refraction. 

Circular  doable  refraction  consequently  appears  not 
to  be  dependent  upon  any  special  arrangement  of  the 
molecules,  but  rather  upon  a  peculiar  structure  of  the 
molecules  themselves,  which  may  no  doubt  betray  it- 
self in  crystalline  bodies  by  the  external  form  of  the 
crystal,  as  in  fact  is  the  case  with  Quartz.  This  opinion 
is  materially  supported  by  the  fact,  that  many  fluids 
possess  the  power  of  effecting  double  circular  refraction,  and 
consequently  the  power  of  rotating  the  plane  of  vibration  of 
rectilinearly  polarised  light. 

The  plane  of  vibration  is  rotated  to  the  right  by 
aqueous  solutions  of  cane-  and  grape-sugar,  tartaric  acid, 


CIRCULAR  POLARISATION.  347 

oil  of  lemons,  and  by  an  alcoholic  solution  of  camphor. 
It  is  rotated  to  the  left  by  oil  of  turpentine,  by  cherry- 
laurel  water,  and  by  solution  of  gum  arabic. 

As  the  rotatory  power  of  these  fluids  is  very  inferior 
to  that  of  quartz,  it  is  necessary  in  order  to  observe 
it  conveniently  to  employ  layers  of  considerable  thick- 

FlG.  185. 


Tube  for  the  reception  of  circularly  polarising  fluids. 

ness,  which  is  best  accomplished  by  filling  tubes  with 
them,  the  ends  of  which  are  closed  with  plane  glass 
plates  (fig.  185). 

If  such  a  tube,  filled  with  solution  of  sugar,  be  placed 
between  the  crossed  Nicols,  the  previously  dark  screen 
immediately  becomes  illuminated,  and  from  the  amount 
of  rotation  which  must  be  communicated  to  the  polari- 
scope,  in  order  that  the  screen  may  again  be  darkened, 
the  angle  may  be  known  which  the  solution  of  sugar 
has  rotated  the  plane  of  vibration  of  the  incident  recti- 
linearly  polarised  light.  This  rotation  is  proportional 
on  the  one  hand  to  the  thickness  of  the  layer,  and  on 
the  other  to  the  amount  of  active  substance  (sugar) 
contained  in  the  fluid,  and  as  it  is  known  that  with  a 
tube  20  centimeters  (7*8  inches)  in  length,  the  rotation 
of  the  plane  of  vibration  amounts  to  l°-333  for  each 
gramme  (15-44  grains)  of  sugar  contained  in  100  cubic 
centimeters  (6-102705  cubic  inches,  or  rather  less  than 
one- sixth  of  a  pint)  of  the  solution,  the  amount  of  sugar 
contained  in  the  solution  may  be  immediately  determined 
from  the  amount  of  rotation  produced  by  the  solution. 


348  OPriCS 

160.  In  order  to  attain  the  greatest  accuracy  in  the 
determination  of  the  amount  of  sugar  contained  in  the 
solution,  an  instrument  is  desirable  which  renders  a 
very  small  rotation  perceptible.  Such  an  instrument 
is  found  in  the  double  quartz  plate  (fig.  186)  first  con- 
FlG  186  structed  by  Soleil.  It  is  composed  of 

two  quartz  plates,  cut  at  right  angles  to 
the  axis  and  cemented  together,  of  which 
one  rotates  to  the  right  and  the  other 
to  the  left,  whilst  each  has  a  thickness 

7   1 

I  of  3'75  mi  limeters.  If  now  a  double 
plate  of  this  kind  be  placed  between 
D°oufb rightaandTft°SrS  the  two  Nicols  the  planes  of  vibrations 
of  which  are  parallel,  and  if  the  image 
be  cast  by  means  of  a  lens  upon  a  screen,  both  halves 
of  the  plate  will  be  found  to  exhibit  the  same  violet 
tint  of  colour.  On  the  interposition  of  the  tube  filled 
with  the  solution  of  sugar,  a  dissimilarity  of  colour  is  im- 
mediately observed  in  the  two  halves  of  the  plate,  one 
half  presenting  a  bluish,  the  other  a  reddish  tint.  The 
plane  of  vibration  of  each  colour  contained  in  white 
light  is  rotated  to  an  equal  amount  in  each  half  of  the 
double  plate,  but  in  the  one  half  the  rotation  is  to  the 
right  and  in  the  other  to  the  left,  as  has  been  indicated 
in  the  corresponding  halves  of  fig.  180.  If  the  prin- 
cipal planes  of  the  Nicol  be  parallel  to  each  other  (in 
the  direction  of  the  arrow)  the  two  halves  must  exhibit 
the  same  tint  of  colour.  A  glance  at  the  figure  above 
alluded  to  suffices  to  show  that  in  this  position  of  the 
Nicol  the  yellow  disappears,  and  that  consequently  a 
violet  colour  must  appear  as  a  result  of  the  mixture  of 
the  remaining  colours. 

As  the  solution  of  sugar  rotates  the  planes  of  vibra- 


CIRCULAR   POLARISATION. 


349 


tion  of  all  rays  to  the  right,  the  rotation  is  increased  in 
the  half  rotating  to  the  right  and  diminished  in  the 
half  rotating  to  the  left;  in  the  former,  therefore,  the 
planes  of  vibration  of  the  orange  tints,  in  the  latter 
those  of  the  green  rays,  appear  in  the  position  previously 
occupied  by  the  planes  of  vibration  of  the  yellow  rays. 
The  former  half  will  therefore  exhibit  a  blue,  the  latter 
a  red  tone  of  colour.  In  order  to  ascertain  how  much  the 
solution  of  sugar  has  rotated  the  plane  of  vibration,  it  is 
only  requisite  to  rotate  the  second  Nicol  till  the  two 
halves  of  the  plates  again  appear  of  the  same  colour. 

161.  As  the  rapid  and  convenient  determination  of 
the  amount  of  sugar  contained  in  a  saccharine  solution 
is  of  great  practical  importance  in  an  economical  point 
of  view,  an  apparatus  has  been  constructed  with  this 
object  in  view,  called  a  Saccharimeter. 

The  Saccharimeter  of  Soleil  has  (fig.  187)  the  previ- 
ously described  double  plate  at  r  bet  ween  the  two  Nicol' s 
prisms  S  and  T,  the  planes 
of  vibrat'on  of  which  are 
fixed  parallel  to  each  other. 
The  change  of  colour  which 
the  tube  filled  with  solu- 
tion of  sugar  intioduced 
at  m  induces  is,  however, 
not  compensated  for  by 
rotating  the  polariscope,  T, 
"but  by  a  highly  ingenious 
compensating  arrangement 
placed  ate  (the  compensator). 
The  rays  emerging  from  m  pass  first  through  a  quartz 
plate  rotating  to  the  right,  cut  at  right  angles  to  the 
axis,  and  then  through  two  wedges,  r  and  o,  cut  from  a 


FIG.  187. 


Soleil 's  Saccharimeter. 


350  OPTICS. 

quartz  plate  rotating  to  the  left  (fig.  188),  and  which  by 
means  of  a  screw,  fr,  can  be  moved  towards  each  other. 


FIG.  188. 


Compensator. 

When  in  contact  they  form  a  quartz  plate,  cut  perpen- 
dicularly to  the  axis,  which  is  of  the  same  thickness 
as  the  first-mentioned  one,  arid  therefore  completely 
neutralises  its  rotation  to  the  right.  If  they  are  moved 
from  this  position  to  either  side,  the  extent  which  the 
rays  have  to  traverse  in  the  two  wedges  together  is 
augmented  or  diminished ;  the  two  wedges  together 
thus  form  a  quartz  plate  rotating  to  the  left,  the  thick- 
ness of  which  within  certain  limits  can  be  varied  at 
will  and  can  be  made  equal  to,  or  larger  or  smaller  than 
that  of  the  quartz  plate  rotating  to  the  right.  The 
alteration  of  thickness  in  each  movement  of  the  screw 
can  be  read  off  by  means  of  the  indicator,  v,  upon  a 
small  scale,  e,  to  the  1000th  of  a  millimeter.  According 
as  the  rotation  of  the  plate  to  the  right,  or  the  rotation 
of  the  system,  of  wedges  to  the  left,  is  allowed  to  pre- 
dominate, the  action  of  the  compensator  is  equivalent 
with  that  of  a  plate  of  quartz  rotating  to  the  right  or 
to  the  left,  the  thickness  of  which  may  be  exactly  deter- 
mined. 

In  order  to  compensate  the  difference  of  colour 
between  the  two  halves  of  the  double  plate,  which  is 
brought  about  by  virtue  of  the  rotation  to  the  right  of 
the  solution  of  sugar,  the  compensator  must  be  arranged 
for  an  equal  amount  of  left-handed  rotation ;  then,  by 
reading  the  scale,  the  thickness  is  obtained  of  a  quartz  plate 


CIRCULAR  POLARISATION.  351 

which  possesses  the  same  power  of  rotation  as  the  saccharine 
solution  under  examination.  And  as  it  has  been  ascer- 
tained by  carefully  made  experiments  that  a  solution 
of  sugar  which  contains  16*35  grammes  (252*44  grains) 
of  pure  crystallised  sugar  in  100  cubic  centimeters  ex- 
erts as  great  a  rotating  power  in  a  tube  20  centimeters 
in  length  as  a  quartz  plate  1  millimeter  in  thickness,  it 
is  only  necessary  to  multiply  the  number  read  off  upon 
the  scale  by  16*35  in  order  to  know  the  weight  of  sugar 
contained  in  100  cubic  centimeters  of  the  solution. 

And  now,  in  conclusion,  let  a  brief  retrospective 
glance  be  cast  upon  the  subjects  that  have  here  been 
treated  of.  The  reply  to  the  question,  What  is  Light  ? 
was  the  end  in  view.  Proceeding  step  by  step  by  the  light 
of  experience,  the  various  phenomena  of  light  were 
considered,  the  laws  investigated  to  which  those  pheno- 
mena are  subject,  and  the  useful  applications  which 
life  and  science  have  made  from  them.  Finally,  a  fact 
was  disclosed  (Fresnel's  interference  experiment)  which 
pressed  home  to  us  the  conviction  that  light  must  con- 
sist in  the  undulatory  movement  of  an  attenuated  elastic 
substance.  Having  arrived  at  this  stand-point,  it  was 
requisite  to  call  a  halt  in  order  to  reconsider  the  phe- 
nomena already  observed,  and  when  it  had  been  ascer- 
tained that  the  previously  isolated  facts  became  in 
succession,  under  this  point  of  view,  united  into  one 
whole,  farther  advances  were  made,  and  new  facts 
obtained  which  threw  additional  light  upon  the  nature 
and  essence  of  light.  The  phenomena  of  polarisation 
demonstrated,  in  point  of  fact,  that  the  vibrations  of  light 
take  place  at  right  angles  to  the  direction  of  the  rays. 
The  last  part  of  this  work  gave  results  that  did  riot  at 
24 


OPTICS. 

first  appear  to  be  capa.ble  of  useful  application  to  the 
life  of  man  until  quite  recently,  when  an  apparatus 
has  been  constructed  of  pre-eminent  practical  impor- 
tance. 

It  is  the  task  of  science  to  strive  after  truth  without 
having  any  secondary  object  in  view.  If  it  remain 
true  to  this  ideal,  the  practical  applications  will  fall 
into  its  lap  as  the  ripe  fruits  of  knowledge. 


INDEX. 


ABS 

4  BSORPTION  lines,  172 
A.  —  of  light,  242 
—  spectra,  173 
A-chromatic  lens,  141,  146 
Achromatism,  134 
/Esculiu,  fluorescence  of,  183 
;Ether,  213 

Alcohol,  index  of  refraction  of,  60 
Angles  of  incidence  and  refraction, 

57 

Angstrom  on  wave-lengths,  270 
Anthracite,  index  of  refraction  of, 

312 
Arc  of  flame,  Volta's,  9 


BARIUM,  spectrum   analysis    of, 
150 
Bartholinus   on    double   refraction, 

282 

Becquerel's  phosphoriscope,  191 
Becquerel  on  wave-length  of  ultra 

red  rays,  280 

Biot's  polarising  apparatus,  307 
Black  cross  of  polarised  light,  for- 

mation of,  326 

—  flame,  163 

Blood,  absorption  spectrum  of,  1  74 
Bunsen's  burner,  3 

—  apparatus  for  absorbing  Sodium 
light,  162 

—  photometer,  24 

—  spectroscope,  148 


spectrum   analysis  of, 
152 

Calcium  fluoride,  184 
•  —  spectrum  analysis  of,  150 
Camera  obscura,  19,  101 


D1A 

Canada  balsam,  index  of  refraction 
of,  60 

Carbonic  disulphide,  index  of  re- 
fraction of,  60 

Carboniferous  strata,  their  relatiou 
to  solar  energy,  256 

Chlorophyll,  absorption  spectrum 
of,  174 

Christiansen  on  anomalous  disper- 
sion of  light,  244 

Circular  polarisation  of  light,  332 

Cobalt,  absorption  spectrum  of,  175 

Colours,  complementary,  120 

—  dispersion  of,  112 
Compensator,  350 
Concave  lenses,  87 

—  mirrors,  40 
Conjugate  foci,  42 

—  points,  81 
Convex  lenses,  79 

—  mirrors,  49 

Copper,  absorption  spectrum  of,  176 

Critical  angle,  63 

Cross,     black,    of    polarised    light, 

formation  of,  326 
Crown  glass,  index  of  refraction  of, 

60 


DARK  rays  of  the  solar  spectrum, 
203 
Deflection,  minimum  of  prisms,  70 

—  without  dispersion,  136 
Determination  of  conjugate  points, 

90 

—  of  the  focal   distance  of  lenses, 
90 

Diamond,  index  of  refraction  of,  60 

—  critical  angle  of  .63 


354 


INDEX. 


DIA 


Diathermancy  of  rock  salt,  203 

Dichroism,  313 

Didymium,  absorption  spectrum  of, 

177 
Diffraction  apparatus,  260 

—  of  light,  258 

Dispersion  of  colour,  112,  140,  242 

—  without  deflection,  137 

—  of  light,  242 

—  anomalous,  of  light,  244 
Doppler  on  pitch  of  sound  and  tone 

of  colour,  245 

Double  prism  of  Fresriel,  345 
Double  refraction,  282 
Drummond's  lime-light,  7 
Dubosq's  lamp,  95 

—  polariser,  325 

—  regulator,  10 
Dutch  telescope,  107 

T7CLIPSES,  cause  of.  17 

Jj     Electric  lamp,  8 

Enlarged  images,  46,  87 

Erbium,    absorption    spectrum    of, 

177 
Esselbach  on  -wave-lengths  of  ultra 

red  rays,  280 

Extraordinarily  refracted  rays,  283 
Eye,  general  construction  of,  102 

FILMS,  colours  of,  273 
Flames  of  candles  and  lamps,  4 
Flint-glass,  index  of  refractiou  of, 

60 

Fluor  spar,  184 
Fluorescence,  183 
Foci  of  concave  mirrors,  41 

—  conjugate,  42 

—  of  lenses,  80 
Fresnel's  double  prism,  345 

—  mirror  experiment,  207 
Front  view  telescope,  110 
Fuchsin,      anomalous        dispersion 

power  of,  243 

pALILEO,  telescope  of,  107 
\J     Galvanometer,  199 
Gases,  spectra  of,  155 

inversion  of,  164 

Seissler's  tubes,  155,  187,  188 


LEN 

Ghost  experiment,  32 
Glass,  critical  angle  of,  63 
Goniometer,  34 
Grating  spectrum,  266 
Gregory's  telescope,  1 1 0 

HEAT,  action  of,  197 
—  measurement  of,  199 

—  curve  of,  in  spectrum,  201 
Heliostat,  32 

Herschel's  telescope,  109 
Hooke's  theory  of  light,  229 
Huggins'  estimate  of  rate  of  move- 
ment of  Sirius,  246 
Huyghens'  principle,  229 

ICELAND  spar,  double  refraction 
of,  284 

Illumination,  law   of,  in  regard  to 
distance,  23 

—  aerial,  47 

—  apparent,  47 
Images,  inverted,  46 

—  virtual,  47 
Incandescence,  2 

Indium,  refraction  of  light  of,  114 

—  spectrum  analysis  of,  153 
Induction  apparatus,  1 54 
Interference  of  light,  316 

—  of  sonorous  waves,  212 
Inverted  images,  46,  86 

Iodine,  absorption  spectrum  of,  173 

TTALEIDOSCOPE,  36 
JV     Kepler's  telescope,  1 04 
Kundt  on  anomalous  dispersion  oi 
light,  244 

T  AMIN^E.  colours  of  thin.  273 
Jj    Law  of  illumination  in  propo? 
tion  to  distance,  22 

—  reflection  of  light,  28 
Lamp,  Drummond's,  7 

—  Dubosq's,  95 

—  electric,  8 

—  magnesium,  7 

—  oxygen,  5 

—  petroleum,  5 
Lantern,  magic,  97 
Lenses,  78 


INDEX. 


S55 


LEW 

Lenses,  axis  of,  79 

—  bi-convex,  78 

—  In-concave,  78 

—  centre  of  curvation  of,  79 

—  convexo-concave,  78 

—  concavo-convex,  78 

—  foci  of,  80 

—  plano-convex,  78 

—  plano-concave,  78 

L'.ght,  absorption  of,  242,  253 

—  dispersion  of,  112,  224 

—  rays  of,  14 

—  rectilinear  propagation  of,  14 
Lime-light,  7 

Lithium,  refraction  of  light  of,  114 

—  spectrum  analysis  of,  150 
Litmus,  absorptiou  spectrum  of,  178 
Lunar  eclipses,  causes  of,  1 7 

MAGIC  LANTERN,  97 
Magnesium  lamp,  7 
Malus  on  polarisation  of  light  by 

reflexion,  311 

Menilite,  index  of  refraction  of,  312 
Meyersteiu's  spectrometer,  144 
Mica,  reflected  light  from  plate  of, 

279 
Microscope,  compound,  103 

—  simple,  102 

—  solar,  98 

Minimum  deflection  of  prisms,  70 
Mirror  experiment,  Fresnel's,  208 
Mirror  sextant,  37 
Mirrors,  concave,  40 

—  convex,  49 

Motion,  modes  of  propagation  of,  210 
Miiller  on  wave-lengths  of  ultra  red 

rays,  281 
Miiller  a  lines,  280 

\TAPFTHALIN,  red    fluorescence 

IN      of,  189 

Newton's  colour  glass,  273 

—  rings,  274 

—  telescope,  109 
Nicol's  prisms,  304 

Nitrous  oxide,  absorption  spectrum 

of,  173 
Nuremberg's  polarising  apparatus, 

308 
Nucleus  of  shadows,  16 


RAY 

OBJECTIVE,  103 
Ocular,  103 

Optical  instruments,  95 
Ordinarily  refracted  rays,  2PS 
Origin  of  light,  248 
Oxygen  lamp,  5 


PARALLAX  of  sun,  18 

-L      Pennine,  dichroism  of,  313 

Penumbra,  nature  of,  16 

Permanganate  of  potash,  absorption 
spectrum  of,  1 74 

Petroleum  lamp,  5 

Photography,  principles  of,  194 

Photographic  action  of  solar  spec- 
trum ;  curve  of,  205 

Photometer,  Bunsen's,  24 

—  Rumford's,  24 
Phosphorescence,  183,  192 
Phosphoriscope,  191 
Plates,  colours  of  thin,  273 

—  bichromate,  176 
Polarisation  of  light,  293 

—  circular,  of  light,  332 
Polarising  apparatus,  303 

—  Biot's,  307 

—  Dubosq's,  325 

—  Norremberg's,  309 
Potassium,  spectrum    analysis    of, 

150 
Principal  axis,  40 

—  comparing,  160 

—  hollow,  71 

—  minimum  deflection  of,  7C 
Principle,  Doppler's,  245 

—  of  conservation  of  energy,  253 

—  of  interference,  217 

—  Huyghens',  229 

Prism,  double,  of  Fresnel,  34-5 
Prisms,  Nicol's,  304 

—  refracting  angle  of,  68 


AUARTZ  crystals,  circular  polar- 
\J,    sation  of  light  by,  335 
Quinia,  fluorescence  of,  187 


RAINBOW,    mode    of   formation 
of,  122 
Rays  of  light,  14 


856 


INDEX. 


REA 


WAV 


Real  images,  81 
Reflecting  goniometer,  34 

—  telescope,  110 

Reflexion,  polarisation  of  light  by, 

306 
Refraction,  56 

—  angle  of,  57 

—  index  of,  60 
Refractors,  105 
Regnlatoi  of  Dubosq,  10 
Resonance,  252 
Reusch's  heliostat,  33 

Rock  salt,  diathermancy  of.  202 
Rose  de  Magdala,  fluorescence    of, 

189 

Rosse's,  Lord,  telescope,  109 
Rubidium,  spectrum  analysis  of,  152 
Rumford's  photometer,  24 


OACCHARIMETERof  Soleil,  349 
O     Selenite,  colours  exhibited  by, 
328 

—  interference,   experiments   with 
plates  of,  319 

Sextant,  37 

Shadows,  nature  of,  15 

—  nucleus  of,  16 

—  penumbra  of,  16 

Sirius,  rate  of  movement  of,  247 
Sodium,  refraction  of  light  of,  1 14 

—  spectrum  analysis  of,  150 
Solar  eclipses,  cause  of,  17 

—  microscope,  98 

—  spectrum,  general  view  of,  205 
length  of,  281 

Soleil's  saccharimeter,  S49 
Sound,  propagation  of,  211 

—  interference  of  waves  of,  212 
Spar,  Iceland,  double  refraction  of, 

284 

Spectra  of  gases,  155 
Spectrometer,  144 
Spectroscope,  Browning's,  149 

—  Bunsen's,  148 

—  direct  vision,  149 

—  Hoffman's,  1 49 


Spectroscope,  dispersing,  169 
Spectrum,  analysis,  149 

—  calorific  action  of,  201 

—  continuous,  118,  250 

—  interrupted,  157 

—  nature  of,  117 

—  solar,  158 

—  thermotic  curve  of,  201 
Spherical  mirrors,  40 
Strontium,  light  of,  116 

—  sulphide,    phosphorescence    of 
192 

Sun,  spectrum  analysis  of,  159,  165 

rpELESCOPE,  Galileo's,  107 
JL      Gregory's,  110 

—  Kepler's,  104 

—  Newton's,  109 

—  Refractors,  105 

Terbium,    absorption  spectrum    of, 

177 
Thallium,  refraction  of  light  of,  114 

—  spectrum  analysis  of,  153 
Theodolite,  106 

Theory,  Huyghens',  229 

Thermopile,  199 

Thermotic   curve   of  the  spectrum, 

201 
Tourmaline  forceps  or  tongs,  314 

TTLTRA  red  rays,  280 
U      Undulations  of  sound,  211 

—  of  water,  213 
TJndulatory  motion,  210 
Uniaxial  crystals,  rings  of   coloui 

produced  by,  328 
Uranium,  fluorescence  of,  187 


VIRTUAL  imatfps,  47,  50, 
Volta's  arc  of  flame,  9 


WATER,  critical  angle  of,  63 
Index  of  refraction  of,  60 
Wave-rays,  215 


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HE  SUN.  By  C.  A.  YOUNG,  Ph.  D.,  LL.  D.,  Pro- 
fessor of  Astronomy  in  Princeton  University.  New  and  re- 
vised edition,  with  numerous  Illustrations.  I2mo.  Cloth, 
$2.00. 

"  In  this  book  we  see  a  master's  hand.  Professor  Young  has  no  superiors,  if  he  has 
rivals,  among  astronomers  in  this  country.  .  .  .  'The  Sun'  is  a  book  of  facts  and 
achievements,  and  not  a  discussion  of  theories,  and  it  will  be  read  and  appreciated  by 
a!l  scientific  students,  and  not  by  them  alone.  Being  written  in  untechnical  language, 
it  is  equally  adapted  to  a  large  class  of  educated  readers  not  engaged  in  scientific  pur- 
suits."— Journal  of  Education,  Boston. 

"  Professor  Young's  work  is  essentially  a  record  of  facts  and  achievements,  rather 
than  of  theories  and  attempts  at  the  interpretation  of  mysteries  ;  yet  the  great  ques- 
tions still  remaining  to  be  answered  are  of  course  discussed,  and  in  a  masterly  man- 
ner."— Philadelphia  Evening  Bulletin. 

"  It  is  one  of  the  best  books  of  popular  science  ever  written,  and  deserves  a  host  of 
readers." — The  Dial,  Chicago. 

"You  feel  throughout  that  a  master  is  leading  you  amid  the  intricacies  and  mazes 
of  one  of  the  most  absorbing  of  studies.  .  .  .  Many  a  one  whose  views  are  hazy  and 
dim  will  find  here  just  that  enlightenment,  without  an  overburdened  technicality,  that 
will  prove  most  useful." — The  Interior. 


T 


HE  STORY  OF  THE  SUN.  By  Sir  ROBERT  S. 
BALL,  F. R.  S.,  author  of  "An  Atlas  of  Astronomy,"  "The 
Cause  of  an  Ice  Age,"  etc.  8vo.  Cloth,  $5.00. 

"  Sir  Robert  Ball  has  the  happy  gift  of  making  abstruse  problems  intelligible  to  the 
*  wayfaring  man '  by  the  aid  of  simple  language  and  a  few  diagrams.  Science  moves 
so  fast  that  there  was  room  for  a  volume  which  should  enlighten  the  general  reader  on 
the  present  state  of  knowledge  about  solar  phenomena,  and  that  place  the  present 
treatise  admirably  fills." — London  Chronicle. 

"  As  a  specimen  of  the  publisher's  art  it  is  superb.  1 1  is  printed  on  paper  which 
entices  the  reader  to  make  marginal  notes  of  reference  to  other  books  in  his  library, 
the  type  is  large,  the  binding  is  excellent,  and  the  volume  is  neither  too  large  nor 
too  small  to  handle  without  fatigue." — New  York  Herald. 


A 


N  ATLAS  OF  ASTRONOMY.     By  Sir  ROBERT 

S.  BALL,  F.  R.  S.,  Professor  of  Astronomy  and  Geometry  at  the 
University  of  Cambridge  ;  author  of  "  Starland,"  "  The  Cause 
of  an  Ice  Age,"  etc.  With  72  Plates,  Explanatory  Text,  and 
Complete  Index.  Small  4to.  Cloth,  $4.00. 

"  The  high  reputation  of  Sir  Robert  Ball  as  a  writer  on  astronomy  at  once  popular 
and  scientific  is  in  itself  more  than  sufficient  recommendation  of  his  newly  published 
'  Atlas  of  Astronomy.'  The  plates  are  clear  and  well  arranged,  and  those  of  them  which 
represent  the  more  striking  aspects  of  the  more  important  heavenly  bodies  are  very 
beautifully  executed.  The  introduction  is  written  with  Sir  Robert  Ball's  well-known 
lucidity  and  simplicity  of  exposition,  and  altogether  the  Atlas  is  admirably  adapted  to 
meet  the  needs  and  smooth  the  difficulties  of  young  and  inexperienced  students  of 
astronomy,  as  well  as  materially  to  assist  the  researches  of  those  that  are  more  advanced." 
— London  Times. 

New  York :   D.  APPLETON  &  CO.,  72  Fifth  Avenue. 


T 


D.  APPLETON  &   CO.'S  PUBLICATIONS. 


HE  NATURAL  HISTORY  OF  SELBORNE, 
AND  OBSERVATIONS  ON  NATURE.  By  GILBERT 
WHITE.  With  an  Introduction  by  John  Burroughs,  80  Illus- 
trations by  Clifton  Johnson,  and  the  Text  and  New  Letters  of 
the  Buckland  edition.  In  two  volumes.  I2mo.  Cloth,  $4.00. 

>  "  White  himself,  were  he  alive  to-day,  would  join  all  his  loving  readers  in  thanking 
the  American  publishers  for  a  thoroughly  excellent  presentation  of  his  famous  book. 
.  .  .  This  latest  edition  of  White's  book  must  go  into  all  of  our  libraries;  our  young 
people  must  have  it  at  hand,  and  our  trained  lovers  of  select  literature  must  take  it  into 
their  homes.  By  such  reading  we  keep  knowledge  in  proper  perspective  and  are  able 
to  grasp  the  proportions  of  discovery." — Maurice  Thompson,  in  the  Independent. 

"  White's  '  Selborne '  belongs  in  the  same  category  as  Walton's  '  Complete  Angler'  ; 
.  .  .  here  they  are,  the  '  Complete  Angler '  well  along  in  its  third  century,  and  the  other 
just  started  in  its  second  century,  both  of  them  as  highly  esteemed  as  they  were  when 
first  published,  both  bound  to  live  forever,  if  we  may  trust  the  predictions  of  their  re- 
spective admirers.  John  Burroughs,  in  his  charming  introduction,  tells  us  why  White's 
book  has  lasted  and  why  this  new  and  beautiful  edition  has  been  printed.  .  .  .  This  new 
edition  of  his  work  comes  to  us  beautifully  illustrated  by  Clifton  Johnson." — New  \  'ork 
Times. 

"  White's  'Selborne'  has  been  reprinted  many  times,  in  many  forms,  but  never  be- 
fore, so  far  as  we  can  remember,  in  so  creditable  a  form  as  it  assumes  in  these  two 
volumes,  nor  with  drawings  comparable  to  those  which  Mr.  Clifton  Johnson  has  made 
for  them." — New  York  Mail  and  Express. 

"  We  are  loath  to  put  down  the  two  handsome  volumes  in  which  the  source  of  such 
a  gift  as  this  has  been  republished.  The  type  is  so  clear,  the  paper  is  so  pleasant  to 
the  touch,  the  weight  of  each  volume  is  so  nicely  adapted  to  the  hand,  and  one  turns 
page  after  page  with  exactly  that  quiet  sense  of  ever  new  and  ever  old  endeared  de- 
light which  comes  through  a  window  looking  on  the  English  countryside— the  rooks 
cawing  in  a  neighboring  copse,  the  little  village  nestling  sleepily  amid  the  trees,  trees 
so  green  that  sometimes  they  seem  to  hover  on  the  edge  of  black,  and  then  again  so 
green  that  they  seem  vivid  with  the  flaunting  bravery  of  spring." — New  York 
Tribune. 

"Not  only  for  the  significance  they  lend  to  one  of  the  masterpieces  of  English 
literature,  but  as  a  revelation  of  English  rural  life  and  scenes,  are  these  pictures  de- 
lightfully welcome.  The  edition  is  in  every  way  creditable  to  the  publishers."— 
Boston  Beacon. 

"  Rural  England  has  many  attractions  for  the  lover  of  Nature,  and  no  work,  per- 
haps, has  done  rs  charms  greater  justice  than  Gilbert  White's  '  Natural  History  of 
Selborne.'  " — Boston  Journal. 

"This  charming  edition  leaves  really  nothing  to  be  desired." — Westminster 
Gazette. 

"  This  edition  is  beautifully  illustrated  and  bound,  and  deserves  to  be  welcomed  by 
all  naturalists  and  Nature  lovers." — London  Daily  Chronicle. 

"  Handsome  and  desirable  in  every  respect.  .  .  .  Welcome  to  old  and  young."— 
New  York  Herald. 

"The  charm  of  White's  '  Selborne'  is  not  drfinable  But  there  is  no  other  book  of 
the  past  generations  that  will  ever  take  the  place  with  the  field  naturalists." — Balti- 
more Sun. 


New  York :    D.  APPLETON   &  CO.,  72  Fifth  Avenue. 


D.  APPLETON   AND  COMPANY'S  PUBLICATIONS. 

LITERATURES    OF   THE   WORLD. 

EDITED  BY  EDMUND  GOSSE, 
Hon.  M.  A.  of  Trinity  College,  Cambridge. 

A NCIENT    GREEK   LITERATURE.      By  GIL- 

•**!     BERT  MURRAY,  M.  A.,  Professor  of  Greek  in  the  University  of 
Glasgow.      I2mo.     Cloth,  $1.50. 

"  A  sketch  to  which  the  much-abused  word  '  brilliant '  may  be  justly  applied.  Mr. 
Murray  has  produced  a  book  which  fairly  represents  the  best  conclusions  of  modern 
scholarship  with  regard  to  the  Greeks." — London  Times. 

"An  illuminating  history  of  Greek  literature,  in  which  learning  is  enlivened  and 
supplemented  by  literary  skill,  by  a  true  sense  of  the  '  humanities.'  The  readerfeels  that 
this  is  no  book  of  perfunctory  erudition,  but  a  labor  of  love,  performed  by  a  scholar,  to 
whom  ancient  Greece  and  her  literature  are  exceedingly  real  and  vivid.  His  judgments 
and  suggestions  are  full  of  a  personal  fresh  sincerity;  he  can  discern  the  living  men 
beneath  their  works,  and  give  us  his  genuine  impression  of  them."  —  London  Daily 
Chronicle. 

"  A  fresh  and  stimulating  and  delightful  book,  and  should  be  put  into  the  hands  of 
all  young  scholars.  It  will  make  them  understand,  or  help  to  make  them  understand, 
to  a  degree  they  have  never  yet  understood,  that  the  Gieek  writers  over  \vhom  they 
have  toiled  at  school  are  living  literature  after  all." — Westminster  Gazette. 

"  Brilliant  and  stimulating."—  London  Athenceum. 

"A  powerful  and  original  study." — The  Nation. 

"Mr.  Murray's  style  is  lucid  and  spirited,  and,  besides  the  fund  of  information,  he 
imparts  to  his  subject  such  fresh  and  vivid  interest  that  students  will  find  in  these  paj>es 
a  new  impulse  for  move  profound  and  exhaustive  study  of  this  greatest  and  most  im- 
mortal of  all  the  world's  literatures." — Philadelphia  Public  Ledger. 

"  The  admirable  perspective  of  the  whole  work  is  what  one  most  admires.  The 
reader  unlearned  in  Greek  history  and  literature  sees  at  once  the  relation  which  a  given 
author  bore  to  his  race  and  his  age,  and  the  current  trend  of  thought,  as  well  as  what 
we  value  him  for  to-day.  .  .  .  As  an  introduction  to  'he  study  of  some  considerable  por- 
tion of  Greek  literature  in  English  translations  it  will  be  found  of  the  very  highest  use- 
fulness."— Boston  Herald. 

"Professor  Murray  has  written  an  admirable  book,  clear  in  its  arrangement,  com- 
pact in  its  statements,  and  is  one,  we  think,  its  least  scholarly  reader  must  feel  an  in- 
structive and  thoroughly  trustworthy  pieca  of  English  criticism." — New  York  Mail 
and  Express. 

"  At  once  scholarly  and  interesting.  .  .  .  Professor  Murray  makes  the  reader  ac- 
quainted not  merely  with  literary  histoiy  and  criticism,  but  viith  individual  living, 
striving  Greeks.  .  .  .  He  has  felt  the  pow'er  of  the  best  there  was  in  Greek  life  and  lit- 
erature, and  he  rouses  the  reader's  enthusiasm  by  his  owi^honest  admiration." — Boston 
Transcript. 

"  Professor  Murray  has  contributed  a  volume  whicli  shows  profound  scholarship, 
together  with  a  keen  literary  appreciation.  It  is  a  book  for  scholars  as  well  as  for  the 
general  reader.  The  author  is  saturated  with  his  subject,  and  has  a  rare  imaginative 
sympathy  with  ancient  Greece." — The  Interior,  Chicago. 

"  Written  in  a  style  that  is  sometimes  spasmodic,  often  brilliant,  andt  always  fresh 
and  suggestive." — New  York  Sttn. 

"  Professor  Murray's  careful  study  will  be  appreciated  as  the  work  of  a^an  of 
unusual  special  learning,  combined  with  much  delicacy  of  literary  insight."— New 
York  Christian  Advocate. 


D.  APPLETON  AND  COMPANY,  NEW  YORK. 


D.  APPLETON   AND  COMPANY'S  PUBLICATIONS. 


M 


LITERATURES   OF   THE   WORLD. 

ODERN  ENGLISH  LITERATURE.  By 
EDMUND  GOSSE,  Hon.  M.  A.  of  Trinity  College,  Cambridge. 
I2mo.  Cloth,  $1.50. 

"  Mr  Gosse  has  been  remarkably  successful  in  bringing  into  focus  and  proportion 
the  salient  features  of  this  vast  and  varied  theme.  We  have  re;id  the  book,  not  only 
with  pleasure  but  with  a  singular  emotion.  .  .  .  His  criticism  is  generally  sympathetic, 
but  at  the  same  time  it  is  always  sober." — London  Daiiy  Chronicle. 

"  Mr.  Gosse's  most  ambitious  book  and  probably  his  best.  It  bears  on  every  page 
the  traces  of  a  genuine  love  for  his  subject  and  of  a  IKely  critical  intelligence.  More- 
over, it  is  extremely  readable  —more  readable,  in  fact,  than  any  other  single  volume 
dealing  with  this  same  vast  subject  that  we  can  call  to  mind.  .  .  .  Really  a  icmarkable 
performance."—  London  Times. 

"A  really  useful  account  of  the  whole  process  of  evolution  in  English  letters- an 
account  based  upon  a  keen  sense  at  once  of  the  unity  of  his  subject  and  of  the  rhythm 
of  its  ebb  and  flow,  and  illumined  by  an  unexampled  felicity,  in  hitting  off  the  leading 
characteristics  of  individual  writers." — London  Athenceiim. 

"  Probably  no  living  man  is  more  competent  than  Mr.  Gos:e  to  write  a  popular 
and  yet  scholarly  history  of  English  literature.  .  .  .  The  greater  part  of  his  lite  Las 
been  given  up  to  the  study  and  criticism  of  English  literature  of  the  past,  and  he  has 
a  learned  and  balanced  enthusiasm  for  every  writer  who  has  written  excellently  in 
English." — London  Saturday  Review, 

"  The  bibliographical  list  is  of  extreme  value,  as  is  the  bibliographical  work  gen- 
erally. It  is  just  one  of  these  books  which  every  reader  will  want  to  place  among  his 
working  books." — New  York  Times. 

"  To  have  given  in  a  moderate  volume  the  main  points  in  a  literature  almost  con- 
tinuous for  five  centunes  is  to  have  done  a  marvelous  thing.  But  he  might  have  done 
it  dryly;  he  has  made  every  sentence  crisp  and  sparkling." — Chicago  'limes-Herald. 

"  A  book  which  in  soundness  of  learning,  sanity  of  judgment,  and  attractiveness  of 
manner  has  not  been  equaled  by  the  work  of  any  other  author  who  has  sought  to 
analyze  the  elements  of  English  literature  in  a  concise  and  authoritative  way." — Boston 
Beacon. 

"  Thoroughly  enjoyable  from  first  to  last.  It  traces  the  prowth  of  a  literature  so 
clearly  and  simply,  that  one  is  apt  to  underrate  the  magnitude  of  the  undertaking. 
Mr.  Gosse's  charming  personality  pervades  it  all,  and  his  happy  iranncr  illuminates 
matter  that  has  been  worked  over  and  over  until  one  might  imagine  all  its  freshness 
gone." — Chicago  Evening  Post. 

"  This  is  not  a  mere  collection  of  brief  essays  on  the  merits  of  authors,  but  a  con- 
tinuous story  of  the  growth  of  literature,  of  which  the  authors  and  their  works  are  only 
incidents.  The  book  is  lucid,  readable,  and  interesting,  and  a  marvel  of  condensed 
information,  without  its  seeming  to  be  so.  It  can  be  read  by  nine  out  of  ten  intelligent 
people,  not  only  without  fatigue,  but  with  pleasure ;  and  when  it  is  finished  the  reader 
will  have  a  comprehensive  and  intelligent  view  of  the  subject  which  will  not  only  enable 
him  to  talk  with  some  ease  and  confidence  upon  the  merits  of  the  principal  creators  of 
English  literature,  but  will  also  point  the  way  to  the  right  sources  if  he  wishes  to  sup- 
plement the  knowledge  which  he  has  derived  from  this  book." — Pittsburg  Times. 

"That  he  has  been  a  careful  student,  however,  in  many  departments,  the  most  un- 
related and  j-econdite,  is  evident  on  every  page,  in  the  orderly  arrangement  of  his 
multitudinous  materials,  in  the  accuracy  of  his  statements,  in  the  acuteness  of  his  crit- 
ical obsarvations,  and  in  the  large  originality  of  most  of  his  verdicts.  He  says  things 
that  many  before  him  may  have  thought,  though  they  failed  to  express  them,  capturing 
their  fugitive  expressions  in  his  curt,  inevitable  phrases." — N.  Y.  Mail  and  Express. 


D.    APPLETON    AND   COMPANY,  NEW  YORK. 


F 


D.  APPLETON   AND  COMPANY'S  PUBLICATIONS. 


LITERATURES    OF  THE   WORLD. 

EDITED  BY   EDMUND   GOSSE, 
Hon.  M.  A.  of  Trinity  College,  Cambridge. 

RENCH  LITERATURE.  By  EDWARD  DOWDEN, 
D.  Litt.,  LL.  D.,  D.  C.  L.,  Professor  of  English  Literature  in 
the  University  of  Dublin.  I2mo.  Cloth,  $1.50. 

"  Certainly  the  best  history  of  French  literature  in  the  English  language." — Lon- 
don Athenceum. 

"  This  is  a  history  of  literature  as  histories  of  literature  should  be  written.  ...  A 
living  voice,  speaking  to  us  with  gravity  and  enthusiasm  about  the  writers  of  many  ages, 
and  of  being  a  human  voice  always.  Hence  this  book  can  be  read  with  pleasure  even 
by  those  for  whom  a  history  has  in  itself  little  attraction."—  London  Saturaay  Review. 

"The  book  is  excellently  well  done;  accurate  in  facts  and  dates,  just  in  criticism, 
well  arranged  in  method.  .  .  .  The  excellent  bibliography  with  which  it  concludes  will 
be  invaluable  to  those  who  wish  to  pursue  the  study  further  on  their  own  lines."— Lon- 
don Spectator. 

"  Remarkable  for  its  fullness  of  information  and  frequent  brilliancy.  ...  A  b^ok 
which  both  the  student  of  French  literature  and  the  stranger  to  it  will,  in  different  ways, 
find  eminently  useful,  and  in  many  parts  of  it  thoroughly  enjoyable  as  well."— Lon- 
don Literary  World. 

"  Professor  Dowden  is  both  trustworthy  and  brilliant ;  he  writes  from  a  full  knowl- 
edge and  a  full  sympathy.  Master  of  a  style  rather  correct  than  charming  for  its  adorn- 
ments, he  can  still  enliven  his  pages  with  telling  epigram  and  pretty  phrase.  Above  all 
things,  the  book  is  not  eccentric,  not  unmethodical,  not  of  a  wayward  brilliance;  and 
this  is  especially  commendable  and  fortunate  in  the  case  of  an  English  critic  writing 
upon  French  literature." — London  Daily  Chronicle. 

"  A  book  readable,  graphic,  not  overloaded  with  detail,  not  bristling  with  dates.  .  .  . 
It  is  a  book  that  can  be  held  in  the  hand  and  read  aloud  with  pleasure  as  a  literary  treat 
by  an  expert  in  style,  master  of  charming  words  that  come  and  go  easily,  and  ot  other 
literatures  that  serve  for  illustrations." — The  Critic. 

"  His  methods  afford  an  admirable  example  of  compressing  an  immense  amount  of 
information  and  criticism  in  a  sentence  or  paragraph,  and  his  survey  of  a  vast  field  is 
b  -th  comprehensive  and  interesting.  As  an  introduction  for  the  student  of  literature  the 
work  is  most  excellent,  and  for  the  casual  reader  it  will  serve  as  a  compendium  of  one 
of  the  richest  literatures  of  the  world." — Philadelphia  Public  Ledger. 

"  Thorough  without  being  diffuse.  The  author  is  in  love  with  his  subject,  has  made 
it  a  study  for  years,  and  therefore  produced  an  entertaining  volume.  Of  the  scholar- 
ship shown  it  is  needless  to  speak.  ...  It  is  more  than  a  cyclopaedia.  It  is  a  brilliant 
talk  by  one  who  is  loaded  with  the  lively  ammunition  of  French  prose  and  verse.  He 
talks  of  the  pulpit,  the  stage,  the  Senate,  and  the  salon,  until  the  preachers,  dramatists, 
orators,  and  philosophers  seem  to  be  speaking  for  themselves." — Boston  Globe. 

"  Professor  Dowden's  book  is  more  interesting  than  we  ever  supposed  a  brief  his- 
tory of  a  literature  could  be  His  characterizations  are  most  admirable  in  their  concise- 
ness and  brilliancy.  He  has  given  in  one  volume  a  very  thorough  review  of  French 
literature." — The  Interior,  Chicago. 

"  The  book  will  be  especially  valuable  to  the  student  as  a  tafe  and  intelligible  index 
to  a  course  of  reading." — The  Independent. 


D.   APPLETON   AND   COMPANY,   NEW   YORK. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

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